What are Invisalign side effects?

All Invisalign is doing is putting forces on teeth to move them to a desired location. Wire braces do the same. While the forces are applied, the teeth may feel tender and wiggle a little. After treatment is complete, the surrounding bone is still soft, so for a few months the teeth continue to wiggle while the bone gets denser and the teeth "settle".
The bite will be affected. Sometimes it requires equilibration when complete, and sometimes the change is minor enough that the bite adjusts on its own.

Invisalign is used to straighten teeth just like braces. You have aligners in your mouth which are like bleaching trays. They may feel strange at the beginning, but you will forget they're in after awhile. They exert pressure on the teeth to move in the right direction. You may feel pressure and some soreness, but it is minimal. Actually, the side effects my dental assistant has from her Invisalign were positive! She lost weight! She did less snacking since she had to remove the aligners before eating and then brush her teeth. Her teeth are straighter than before and her oral hygiene is great! So look at the positive side...you will have straight teeth and you can also use the same trays to whiten them! You will snack less, have better oral hygiene and may lose weight!

Like any type of medical or dental treatment, your body will go through a process of adjustments.
For Invisalign, this may include the getting used to the bulkiness of the attachments that sometimes are needed to help the aligners move the teeth.
A major adjustment is also the soreness your jaws will feel as the bone softens and the teeth move. The aligners will not fit just right at first, either, as the teeth need to shift into position the aligners want your teeth to be in.
Ask your dentist specifics of what to expect, but as treatment commences you will get used to these sensations and treatment should get easier as you go along.