I'm here to tell you it's NOT madness (and it's not Sparta either). Having wielded the Eyelander for 90% of the time since it's release, i'm now here to pass on my secrets to proper, effective usage of this sword and shield combo that the drunk Scottish explosives expert decided to bring to a fight filled with miniguns, automated sentry turrets, rockets, and "magical" healing devices instead of his remote detonation charges.
Demoknighting sure has changed. I practically have to rewrite everything. May as well.
Overview
A Demoknight is generally a Demoman who forgoes the Sticky Launchers and rather opts to carry one of the three (currently) avalible shields to battle. By doing so, the Demo loses the versetality and manuverbility gained by having stickybombs as part of his arsenal but instead gains a different degree of mobility and a huge boost to personal defenses and melee combat. There are several combinations of sword, shield, and primary that provide high flexibility with the setup, but it burns down to one thing: running at people and smashing them over the head with whatever's in your hands.
Initial Loadout Choices
Shield
*Essentials (Applies to all shields)
Simply equipping either shield gives you passive damage resistance to fire and explosives. To clarify, that damage resistance applies to these weapons:
Fire
Any Flamethrower
Any Flare Gun
Sharpened Volcano Fragment (afterburn, initial attack is Melee damage)
Burning Huntsman Arrows (afterburn, initial attack is Bullet damage)
Cow Mangler 5000 Charge Shot (afterburn, initial explosion is Explosive damage)
Hadouken (A demo must have 4+ heads and must be overhealed or under a defensive buff to survive anyway)
Armageddon (Rainblower Taunt, same deal as Hadouken, though if enough people are caught in the blast the damage will be reduced)
Huo-Long Heater (the blazing aura, the bullets are still Bullet damage)
Explosive
Any Rocket Launcher (Cow Mangler 5000 included, Rocket Jumper excluded)
Any Grenade Launcher
--I am not sure what the damage from the Loose Cannon is considered. I assume explosive, due to the gibbing effect.
Any Sticky Launcher (Sticky Jumper excluded)
Ullapool Caber (explosion; initial swing, and swings after explosion are Melee damage)
Level 3 Sentrygun Rockets
Kamikaze (Same deal with Hadouken)
--Self-inflicted blast damage is NOT reduced
--The Classic is still Bullet damage, despite the death animation being a gibbing.
In addition to the nice perk of damage resistance, both shields grant you the ability to charge forward at 2.5 base speed (750 hammer units/second) (for comparison, Scouts run at 1.3 base speed) for about a second, covering a lot of distance in the process. (the speed is reduced to 1.8? (638 hammer units/second) with the Scottsman Skullcutter. If the Claidheameh mor is equipped, the charge will last longer, increasing distance of charge by 25%). Unless you wear Ali Baba's Boots or the Bootlegger or are using the Tide Turner, it is very difficult to make turns while charging. If you are wearing either footwear, it's easier, but don't expect to turn on a dime. If you use the Tide Turner, you have full control of turns and can even spin in circles! While charging, swinging your melee weapon will end the charge and will deal additional damage based on how long you were charging. Your weapon will mini-crit (+35% damage) about halfway through, and close to the end, your weapon will critical (+300% damage). Firing a Grenade Launcher (if equipped) while charging will not end the charge, nor will the grenades gain crit bonuses. With the exception of a Pyro airblast, anything ending your charge, be it a solid object, a player, a melee swing, or an explosion, will drain the remainder of your charge meter (unless you score a kill using the Tide Turner, in which case your charge meter is instantly filled). Your charge meter refills in 10 seconds (less with the Splended Screen), upon respawn, or reaching a Resupply cabinet. If a Pyro airblasts you mid-charge, your charge meter will refill from the point at which you were airblasted.
--A bug that's been present since the Splendid Screen's release, if you run into a player at any distance as you perform your melee swing, you will be given a critical melee swing, even if you traveled no distance.
Finally, all shields now do bash damage at any distance should you impact with an enemy. The damage is relative to the amount you've covered so the further you go, the more damage you'll deal.
*Chargin' Targe
+50% Fire Resistance
+30% Explosion Resistance
The original demoknight shield, and my personal favorite, having this shield dramatically improves your survival against Soldiers, Pyros, and other Demos who opted not to bring a sword/shield. Choosing this over the other shields will grant you higher survivability as opposed to increased damage dealt.
--When impacting a player at maximum charge distance (the distance required is when your window for critical hits is open), the shield bash will deal 50 damage and is considered a Bullet attack. If you are wielding an Eyelander, Headtaker, or Nine-Iron, the damage will be boosted by 10 for each head you have collected, up to five for a maximum damage of 100.
--The Targe is not recommended for Medieval mode due to the lack of fire and explosives available.
*Splendid Screen
+20% Fire Resistance
+20% Explosion Resistance
+70% Bash damage
+50% Recharge rate
A more offensive shield, this one provided less than half of the resistance offered by the Targe. In exchange, your shield bashing is dramatically improved with a 70% charge impact bonus and a faster recharge time.
--Bashing with this shield at max distance causes 85 damage. If you are wielding an Eyelander, Headtaker, or Nine-Iron, your damage will be boosted by 17 per head collected, up to five for a maximum damage of 170.
*The Tide Turner

+15% Fire Resistance
+15% Explosion Resistance
100% Turning Control while Charging
Melee kills restore 75% charge. (you do not have to be charging; shield bash kills count for this)
Taking damage while charging reduces remaining charge.
Only grants mini-crit boosts from long range charges
The shield with the least amount of resistances, this shield isn't a good option for survival, however the other effects of this shield make it stand out though. Full turning control means you can run circles without having to worry about abusing exploits to do so. The big deal is the kill recharge aspect though. When you kill someone with a melee attack while charging you instantly refill almost all of your charge meter and can dash again. This allows for chain-killing as well as hit-and-run tactics to be employed with little difficulty though you might have to take multiple swings at someone. Recent updates have made it that if you take damage while charging you will have your remaining charge reduced. This means that if you get shot while charging at someone, you may not reach them. As such, use the Tide Turner against unaware enemies so you don't run the risk of being stopped in your tracks.
--Shield bash damage with the Tide Turner is the same as the Chargin' Targe.
Primary Weapons
There are a few to pick from.
*Grenade Launcher/Reskins
The most basic demo ranged weapon and probably the easiest to use. This allows you to lay down a barrage of grenades over medium distances between charges and gives you a very powerful, if somewhat inaccuracte, weapon to use when you need. A somewhat slow loader, try and keep it loaded as often as possible and ready whenever you need it, as without your stickybombs, this is your primary source of explosive damage. 3 well-aimed shots from this will usually take down a level-3 sentry if the Engineer is not guarding it (and if he is, he'll likely be caught in the slash damage)
*Loch-n-Load
+20% Damage to buildings
+25% Projectile Speed
-25% Magazine Size
-25% Explosion Radius
Bombs shatter on surfaces
The Loch-n-Load isn't quite as strong as it used to be. It's still a formidable launcher but many of the perks of the weapon have been removed or reduced. The Loch still fires grenades at a higher velocity which means you can still make longer shots but it no longer has a damage bonus. Conversely it also no longer has the self-damage penalty it initially came with (but you can still 2-hit kill yourself if you use the Eyelander) and it now has a third shot for some reason. It's role has been relegated to long-distance building destruction which is still very useful for Demoknighting. The damage of the launcher is the same as the stock and the high speed shots are still rewarding if you can lead your targets but it's no longer the force of destruction it used to be.
--Now that there's three shots, you can win a fight with a Heavy at full health with no overheal if you can land all three shots (barring criticals).
*Ali Baba's Wee Booties/Bootlegger
+25 Max Health
+200% Turning Speed
+10% Movement Speed
Melee kills refill 25% of your charge meter. (you do not have to be charging; shield bash kills count for this)
No ranged attack capability
For those who want to go pure melee, these are for you. equipping either footwear removes your Grenade Launcher, forcing you to rely on your charging and melee attacks. The plus here is that the boots increase your max health by 25, negating the penalties of the Eyelander, or boosting your health to 200. On top of that wearing either boot grants improved turn control, allowing you to make much tighter turns, often surprising your enemies and allowing for better evasion. If your charge is down don't be afraid to run away as many will simply backpedal away from you and shoot. Without a ranged attack you'll end up getting killed if you pursue one person too long or too far.
--If you use the Tide Turner, note that the turning control boost is redundant, as the Tide Turner has no turning hindrance whatsoever. You will still recover charge on a melee kill which in tandem with the Tide Turner will grant full charge refills on each kill.
*Loose Cannon
Cannonballs have a 1 second fuse that can be primed by holding down Primary Fire
--Holding primary fire too long causes a misfire (similar to the Beggar's Bazooka) that does close to 90 damage to yourself and decent damage to any enemy directly next to you.
Cannonballs knock back players
+20% Projectile Speed
No explosions on direct hits
Added with the 2012 Winter update, this grenade launcher provides a very interesting alternative to the stock launcher that seems to require a fair degree of skill beyond spamming around corners. While that tactic is still possible, it's less effective due to the damage penalties for missing. This weapon has some clear disadvantages for Demoknighting, mainly pushing enemies out of your way on direct hits, though with proper timing and priming, you can potentially hit enemies twice in one shot doing a lot of damage. The bombs also keep going when they hit people, allowing you to literally bowl over large groups traveling in straight lines or tight passages. Another useful note of this launcher is that knockback on direct hits will push Ubercharged enemies so you can use this launcher to hold back Ubers, similar to a Pyro.
--An added perk of this grenade launcher, should you be willing to take a strong hit: you can perform a very powerful grenade jump by misfiring your grenade and aiming down and to the right at an angle behind you (something like a 4 or 5 o'clock position from facing front). If you are willing to tough out the brunt of the self-inflicted damage, this launcher can add a lot of mobility for going airborne and when charges are down. If you intend to do this, I recommend not using the Eyelander to keep as much health as possible, or wait until you've collected enough heads to soak up some of the damage.
--Added with the July 18th patch, if you can successfully hit someone with both the bomb itself and the explosion, the explosion will perform a special sound effect and deal mini-crit damage in addition to the impact damage. Without damage spread or resistances this equates to 131 damage on a double-hit.
*The B.A.S.E. Jumper

Parachute enables slow fall
No ranged attack capability
Introduced in the Love & War Update, this parachute is neat....but I would advise against it for Demoknighting. Without Stickybombs it's difficult to get any air (you'd have to ramp jump to take full advantage of it). The parachute also leaves you defenseless against ranged threats without boosting your health like the shoes do. The only real advantage you can get out of equipping this is a way to avoid fall damage. If you're crazy enough to leave your shield behind, using the Sticky Jumper can make you an aerial melee threat. Your speed is capped while descending though (slower than two stickies can send you) and this combo leaves you with no ranged ability and no damage resistance. With the proper weapons though (Skullcutter, Pain Train) it can be an interestingly difficult experience.
*The Iron Bomber

Grenades have little bounce and roll.
-15% Explosion Radius
A new launcher added for Smissmas 2014, the grenades fired from this one don't bounce or roll a whole lot (despite being perfectly spherical) at the cost of a slightly smaller blast. It has the same damage as the stock launcher and the same airborne physics so you can use it in a similar manner. What I think this launcher is good for is cutting off escapes; in essence you're firing what amount to timed mines since the balls don't roll very far when they hit the ground. If you can't get a hit on the person you're aiming for, you'll probably leave a few explosives behind them which will still hurt a lot should they try to run. You can also fire them into windows and at ceilings behind cover to pressure enemies in hiding with more reliability than the stock launcher.
--The lack of bounce and roll allows you to easily use this launcher as a means to grenade jump as the bombs don't roll away unpredictably. This launcher can add much needed vertical movement options to a demoknight but remember the bombs are still on a 2.3 second fuse.