Flamethrower: The flamethrower can be immensely powerful when used correctly. When used incorrectly, it's more of a menace to your own team than to your enemies. The most important thing to remember is that the flamethrower is a short-ranged weapon, suitable for ambushes because your victim will be blinded by the flames and generally unable to retaliate before they're dead. The flames burn for a few more moments after you hit someone, and do an additional 25 damage or thereabouts. The flamethrower is best used with short passages and blind corners where you can get the first shot on people while they run by; even a short burst can kill someone at full health. It can also be used well offensively, but there are a few things you can't forget. First, your speed is drastically lessened while firing. That means it's more difficult to set yourself on fire... but also means enemies will be able to retreat and take you out with grenades or by blindly firing through your impressive-looking but ineffective wall of flames. Second, never, never, NEVER take the second rank in a charge when you have a flamethrower. Firing into a melee is a good way to kill teammates and lose friends. Furthermore, even though tight quarters are your friend be careful about firing at walls. The flames will rebound, and you aren't immune to setting yourself on fire. Finally, forget about using the flamethrower on large outdoor maps - it just isn't up to par.
MG42: The only way to use the MG42 effectively outside of point-blank range is to lie prone and engage the tripod (alt-fire). This zooms in slightly but prevents you from moving the gun more than about 20 degrees in any direction. In other words, make sure you have someone to watch your back when you're using the MG42 because you're incredibly vulnerable from every direction but one. In many ways, the MG42 is the opposite of the flamethrower. It works best, unsurprisingly, facing into long corridors and choke points. It's also a long-range weapon, and depends on sheer rate of fire to make up for the inaccuracy. Finally, it's almost entirely a defensive weapon. Note that this doesn't mean it can't be used on the attack - in fact, one of the best ways to use it is to set up outside of a heavily trafficked area and "defend" it against the people that should be there keeping you out. A well-placed soldier using the MG42 can pin down a section of the map by themselves for some time, and with good support from field ops and medics there's little they can't survive.
Thompson/MP40: Honestly, there's not much to say about the sub-machinegun. There's little use for a soldier with one, because any class (other than Covert Ops) can carry one and perform other useful functions. If you want a Thompson and ammo, it's really best to pick Field Ops so you can contribute something else to your team.
Soldiers have semi-exclusive access to the Heavy Weapons skill, while other classes can gain experience by using the mounted MG42s found in the levels, but aren't likely to come by it as quickly or easily as a true soldier. So here's everything you need to know about the Heavy Weapons skill, taken from the manual. (if you want to read the entire thing, check the Wolfenstein: Enemy Territory group in the start menu)
This rewards players for kills with Heavy Weapons. Players of any class will earn 3XP for a kill using an Emplaced or Mounted MG. Soldiers earn 3XP for kills with the Mobile MG42, Panzerfaust, Flamethrower or Mortar. You earn 3XP whether the kill is due to explosive splash damage or a direct hit.
Heavy Weapons Level 1: Improved Projectile Resources
Your combat experience allows you to use your projectile weapons with greater ease. Firing a Panzerfaust or Mortar will now take 1/3rd less Power Bar than previously.
Heavy Weapons Level 2: Heavy Weapon Proficiency
Your technical know-how means that your overheating Emplaced or Mobile MG will cool at twice the normal rate.
Heavy Weapons Level 3: Improved Dexterity
You've been lugging heavy chunks of metal around the battlefield for so long, your speed penalty is now decreased. You will still be slowed when firing the Flamethrower, but when carrying it or your other weapons - your speed is now faster.
Heavy Weapons Level 4: Improved Weapon Handling
Such is your skill at toting weaponry, you are now able to handle a Light Weapon in one handed slot, freeing up the two handed slot for an alternate Heavy Weapon. This means you can now carry an SMG and a Mortar, for instance.