Heavy - very slow mid-range area denial, extremely reliant on HP. Has a minigun and a shotgun. As minigun requires rev-up time, shotgun is very rarely used. After revving up a minigun (~one and a half seconds) heavy can kill any class at close range near-instantly and most classes at mid-range at the cost of slowing himself down even further. His minigun is not effective at farther than a certain range, meaning that getting outranged is his weakness. What's more, he is forced to always face the way he fires, making spies extremely effective. Very fast time-to-kill around him one target at a time, but weak to many kinds of things like Soldiers/Demomen playing peek-a-boo with cover to outdamage him. Constant influence projected on the battlefield, compared to their variable.
Engineer - structure-reliant area denial, dependent on ammo pickups. Has a shotgun, pistol, sentry turret, dispenser for replenishment and a teleporter for team support. All structures consume metal and, more importantly, time to create. Engineer is a separate actor from his buildings - he acts like a weaker version of scout, as damage from his shotgun does not rise above a certain point the closer he is to the target. His sentry, however, applies constant influence on the battlefield and combined with his own adaptability he is able to maintain area denial of his sentry's range provided it's feasible to do so.
Sniper - far-range assassination specialist. Has a sniper rifle and an SMG. Sniper Rifle can store charge when aiming down it's sights, lowering your movement speed and zooming you in. Can kill mid-HP classes without overheal instantly by shooting them in the head. Very weak to close-range attacks, as he has no ways to deny area near him but his low-damage SMG and risky Sniper Rifle headshot attempts. Also weak to proper spies. His reliable method of area denial is shooting at mid-to-far area of his cone of vision while area around him is clear.
Medic - team-wide health kit on wheels. Has a syringe fun and a medigun. Syringe gun is used while retreating to damage and repel an enemy, denying area directly behind his retreat or alternatively denying area based on his predictions around him. Medigun serves as means to gamble on the fact that your teammate can live longer than an enemy when their threat zones overlap, making them win in a normally bad situation or alternatively passively resupplying your team via overheal. Medic does not threaten area around him with Medigun, thus someone else must do it for him. If he survives long enough, he can activate Ubercharge to nullify all enemy damage with predictable results. Invaluable because of potential to nullify effects of enemies's presence. As long as medic remains alive for long enough to build Ubercharge, he can gain a lot of advantage. Such methods of nullifying enemy's shooting and dodging skill can turn a game from a tactics contest to a strategy contest.
Spy - close-range assassination specialist. Has a revolver, knife, disguise kit, sapper and invisibility watch. Revolver is a close-range weapon that deals more damage the closer you are, but nowhere near enough damage to out-DPS offense classes. Knife instantly kills if struck in the back, making for a good combination with a disguise kit, that allows him to make it seem like he's on an enemy team. Sapper disables buildings and eventually destroys them and invisibility watch can make it seem as though he's not there. Last of the three classes with unorthodox area denial ranges, Spy relies on distractions - such as enemy being too focused on whomever he's fighting to exist. His threat range is behind the enemy when they don't see him and when they see him he's usually really dead, has a revolver out or is making a getaway.
Each of those classes sports it's own method of applying territory control to a part of the map, usually meaning that whomever's in their range dies really fast, assuming that skilled players are using them. Certain ways to control and remove opposition listed here could be used, improved and refined further to make a really fun vidya, as having multiple paths of dealing with a difficult enemy is key for including strategic elements into your game's skill curve, which our gamedev industry that's pandering to the lowest common denominator seems to lack right now.