I haven't played UMK3 since MK9 released. I will say that with the characters you're using you'd do well to learn full combos off AA attempts. Combos that start in the air to a tremendous amount of damage.
Scorpion - AA RH, teleport, HP, spear, HP HP HK b+HK
H Smoke - AA RH, teleport, HP, spear, HK D+LP D+HP, run-in HP, JK airthrow or
AA HP into spear, HK LP, spear, HK D+LP D+HP, run-in HP, JK airthrow
Kabal - AA HP into dash, HP HP, JK into air fireball.
Stryker - (never played him much but I'm pretty sure you can) AA HP into gun into his mid-screen infinite.
For crossover attempts the easiest thing to start with is run-under sweeps. I always found universal anti-air tactics like these fairly easy to pick up on. AA HP into combo varies from character to character but not too difficult to master.
If AA HP combos give you trouble, you can always land a standing HK without trouble. It's very effective and easy.