Shadow Demon is well known as one of the most disruptive (har har) heroes out there, and can completely turn the tide of any teamfight with last second saves, a BKB piercing slow, and the ability to remove key enemies from a fight entirely.
However, he's also a walking delete button for most enemy carries starting at level 6, only getting even more embarrassing once he has the mighty Meme Hammer in his clutches. With Meteor Hammer, you can win just about any 1v1 fight going well into late game. As your enemies scale in power, so do their illusions, so the stronger they get, the faster they die at your hands.
Avoiding Shadow Poison until midgame may seem counterintuitive, but once you land that first satisfying combo kill, you'll understand entirely. Also in this current meta, utility trumps straight up damage from supports and cores, so the shorter cooldown on Disruption paired with the ability to immediately remove 40% of an enemy's hp when starting a fight by level 9 more than makes up for the lack of early Shadow Poison harass.
Starting at level 6 and reaching full power at level 9, your combo of main abilities is devastating to any low hp/high damage output character. Against most characters, you initiate with Disruption, hit with Soul Catcher while they're bubbled, then hit them with Demonic Purge the second they come out to maximize the effect of the slow - in this case, the damage burst at the end of purge will rarely even be needed to secure the kill. If it's safe to do so, you can hang around and add right click damage, but it's not really necessary - their illusions will generally deal enough damage to them while they're slowly trying to walk away.
The caveat here is that if it's a hero with blink or blink-initiation ( Anti-Mage, Phantom Assassin, Queen of Pain etc), your combo is pretty worthless since they'll be able to just blink out before their illusions have a chance to do any substantial damage. However, that option can also be dealt with if you don't show up empty handed...
In a case of incredible convenience, the cast point and channel time of Meteor Hammer just so happens to equate exactly to the duration of Disruption. Once you have your mighty Hammer in hand, all opponents are equally out of luck.
The full combo looks like this:
On top of the combo potential, Meteor Hammer also provides you with everything you need to make it through the early game. Starting with Sage's Mask shortly followed by Ring of Regen gives you enough sustain to stay in lane - then once you complete hammer, +3 mana regen is more than enough to keep you topped off since you won't be spamming shadow poison. The 12 strength and +5 health regen also gives solid survivability for early fights.
Adding Shadow Blade turns you into a roving assassin, allowing you to pick off solo-farming carries or reposition to take out the backline in a teamfight. Usually Disruption gives you enough of a chance to get away, but Shadow Blade also gives you an extra out in case you get jumped.
Once you're solidly in mid-late game, the addition of Aeon Disk allows you to stay in fights longer, and soak up some damage for the rest of your team. Since most of your abilities either deal damage on a delay or are pure disable, the fact that Aeon Disk interrupts your own damage output really doesn't matter, making it an ideal fit.
After those items, it makes sense to just fill out your build with more utility based items. Scythe of Vyse is ideal if you're making enough gold to get it in a timely manner, but generally it'll be better to go for Eul's Scepter of Divinity to have that extra utility available earlier. If the other team has very strong right-click, Heaven's Halberd can also be a great next item instead. No matter what you wind up building, your aim is to provide your team with a solid window to take control of a fight by incapacitating as many of the enemy as possible at once, or chain-disabling one particularly dominant enemy.
Unfortunately, your ability to delete enemies on command gradually drops off as Black King Bars and other survivability items come out, and as teamfights become more common than solo encounters. So as you shift into the late game, your priorities shift as well.
Instead of trying to combo Soul Catcher, just try to hit as many enemies as you can with it at the beginning of the fight for that sweet 40% hp reduction.
As for Disruption, the temptation is to always use it on enemy carries for the powerful illusions they'll create - however, depending on the enemy team lineup, Disruption may actually be more useful to remove a key disabler before they can influence the teamfight.
Meanwhile, since Demonic Purge works through Black King Bar (and any spell immunity), you can reliably cast Demonic Purge on the carry every time - at 90% slow your team should be able to kite them while they secure the kill.
If you have safe space and time to channel, try to either catch as many enemies as possible in the Meteor Hammer radius, or preventatively cast it over your backline carries/disablers to stun anyone that tries to jump them. Otherwise, focus on using your other active items and create some space for yourself to spam Shadow Poison until you have room to channel Meteor Hammer or Disruption comes off of cooldown.