The best way to do this is go into settings, click key bindings, and change melee to E. This makes it alot easier than using whatever key they used to have (idk, I've used e for so long)
After that, simply jump, and press melee. It gives you a speed boost in whatever direction you're looking, even up. On that note, you can separate a double jump in between the boost, so you jump, melee, jump (JMJ). With that, you can go into an AI match, look up at the tower, jump, melee, jump and you're at the roof. The top speeds I got from boosting was 20m/s looking forwards and up, 25m/s looking down while falling, and the strangest one, 30m/s after doing a JMJ upwards diagonally.

For this, press crouch and it speeds you up from 8m/s to 10m/s. It doesn't do that much, but doing it right before and after landing a JMJ lets you keep a little bit of speed, but it wears off quickly.

Essentially, get a grenade launcher, rpg, or just the recharging grenades and jump while looking at the ground, shoot, and boom (no pun intended). Don't do this, as it would drain half your health and JMJing into the sky works way quicker, is safer, and is more reliable.

Goomba Stomping
It's essentially Trolldier in TF2, jump over your target and melee them from above.

Strafing
Strafing works as you'd expect, JMJ, and hold D and move your mouse right, and vice versa.

Wallruns
You can run on walls, and jump/doublejump/melee boost off. Jumping back onto the wall lets you repeat this, which is a good tactic to get up towers in multiplayer.