1- pousser → he dragged her out to the door and shoved her into the street → she shoved as hard as she could.
2- to shove sb out of the way : écarter qn en le poussant
3- fourrer → We'll shove an extra paragraph in here → he shoved a cloth in my hand. Il m'a fourré un torchon dans la main.
4- to give sb/sth a shove : pousser qn/qch → the car won't start. Can you give it a shove ?