Learning the basics of rocket jumping will be incredibly helpful and enable you to move around the map/get into favorable positions much faster.

Soldier, like demoman, also has a lot of area denial capability that lots of players don't take advantage of. If you're aware of an enemy team around a corner, try to get splash damage on that position to make the enemy team softer when they eventually push for your teammates. You have plenty of ammo- use it!

Combining this with rocket jumping, learn what sections of the map you can get advantageous angles on blenemies by rocket jumping. Lots of buildings in TF2 don't have invisible walls above them, so rocket jumps can get you angles up above the buildings to take distant shots at engineer nests.

On engineer nests, don't just pelt the sentry in a 1:1 scenario with the engineer healing if he has a dispenser behind it. Try to get splash damage on the dispenser and the engineer before the sentry (this changes if you have team support). The direct hit is an amazing weapon at taking out sentries so make a loadout with it.

Personal thing, but I find the original much easier to use than the stock launcher when it comes to placing shots, so give it a chance if you haven't and see which ones feels better to you.

If you have specific questions feel free to ask and I'm glad to weigh in.