Formal:
* Enforce
* Mandate
* Prescribe
* Dictate
* Force
* Inflict
Informal:
* Push
* Stick
* Unload
* Palms off
* Heave
Negative Connotations:
* Thrust
* Obtrude
* Butt in
* 强加 (qiángjiā) (Chinese) - "To force upon"
The best synonym to use will depend on the specific situation and the intended meaning.
For example, "impose" can be used to describe a government imposing a new law, or a person imposing their opinions on others. The synonym you choose should reflect the nuance of the situation.