The power in your hit comes from transferring your momentum to the ball. If your momentum is low, the hit will be less powerful. The part of your car that you hit the ball with can dull the effect of your momentum, but your momentum is still the deciding factor in how powerful your shot will be.
Dodges/flips seem very effective at making high-powered shots because they actually give your car a very high momentum in a circular motion for a brief period of time, as it needs to do a complete 360 degree rotation very quickly. If you touch the ball with this quick rotation, it gets your car's momentum in that direction upon contact, which is typically a very high momentum.
Without dodges/flips, however, you'll need other methods of having a high momentum at the moment of impact. When driving on the ground, the goal for a powerful shot is to go supersonic prior to impact. When performing aerials, however, that's probably not an option.
High momentum with aerials is more about preserving whatever momentum you start with rather than expecting to gain momentum. The entire time you are airborne, gravity is reducing your momentum (unless your goal is to shoot downwards), so you want a high starting momentum so that gravity's overall effect is weakened.
For making sure that you get a good starting momentum before gravity drags you down:
- Make sure to line up your aerial on the ground before going up. Midair adjustments frequently kill your momentum.
- Pull back on your analog stick prior to jumping. This will get your car pointed the correct direction faster than attempting to adjust even a split second after jumping. The sooner you are pointing up, the sooner your boost is contributing to upward momentum.
- If you're not going to be able to dodge/flip at the end of your aerial, use the second jump once your car is correctly oriented in the air. This requires you to stop pulling on the analog stick for a moment so that your jump sends you straight up rather than flipping. This second jump will help to negate gravity early in your long aerial (and don't let go of your boost while doing this!).
- When it comes time to actually contact the ball, make sure to pound on the boost to add whatever extra momentum you can squeeze out of it.
- When possible, try to hit the ball from underneath rather than straight forward. It lets you contact the ball quicker, meaning that you spend less time fighting gravity and losing momentum. The sooner you make contact, the better.
tl;dr Preserve more of your speed in midair if you want stronger midair hits. The ball's speed is directly proportional to the speed of the object that is hitting it.