If I move out before my lease is up, can I be charged for any remaining months if the apartment is re-leased before the remaining months on the lease contract?

You can be charged rent for any months the apartmenbt is vacant. The landlord should make serious attempts to rent but you owe for vacant months and any of his advertising expenses. You can try to negotiate a better deal but this is what the law states.

You are always responsible for the balance of a lease if you leave early without making an agreement. The exception to this is for military personnel as most states have laws to accommodate.

However, most states have laws against double dipping which means the landlord can't collect twice for renting the same place. So once a new tenant moved in, your responsibility ends. Most states require that a good faith effort be made to find a new tenant.

You are better off trying to negotiate a buyout.

Agree, but the military exclusion rule usually requires proof they have been deployed.