Can I sue my roommate for breach of contract for letting her 21 year old son move in the house we share

You don't have a contract w/your roomie----presumably the only contract is w/the landlord. If you are unhappy w/your roomie allowing her son into the house, talk it over your roomie. If the property manager is unwilling to compel your roomie to follow the contract between them, I suppose you may have a verbal breach of contract w/your roomie where you promised one another you wouldn't let anyone else live there and you might be able to bring a small claims court action out of that though showing your damages arising from the kid being there will be tricky. best wishes

You have some inconsistent facts as you speak of an existing lease and a refusal to sign a lease with him on it. In theory you could sue to LL enforce the lease terms to force the son out. However, the remedy may be eviction of all of you if he won't leave due to breach by your roommate. It simply a matter of who pulls out thier wallet to hire a lawyer first in this instance. LL's typically gamble that tenants are all puff no punch.

You can break any contract, but you may be responsible until it is mitigated.