Looked through several VehicleBody3D tutorials over the web, but still no luck
Problem - a car keeps trembling while driving, when turning - also gets too big right or left roll. Why it could be so? What I'm doing wrong?

I don't need it to be ultra-realistic, driving exprience like in GTA 3:SA would be totally enough for me.

My project is here: https://github.com/32kda/vehicle_sample

Seems I've found a solution - changed Roll Influence for all wheels from 0 to 1, no more trembling after that

Maybe you should give Jolt a shot, I heard it's relatively more stable, predictable compare to official physics.