What laws/ rights can I use against him to keep him out my room?
Who owns the house (or rents it if it is being rented from a third party)?
If your stepdad does, you can't keep him out of your room.
Unless you own the house (or rent it from a third-party), you don't have the right to exclude anyone from your room unless the owner (or tenant on the lease) gives you permission to do so.
As a practical matter, if your stepdad and mom live in the house as husband and wife, you will not prevail in any effect to take legal action, either through a trespass lawsuit or a criminal trespass complaint, merely because he goes into your room. He will be found to have implied permission from the owner (or tenant on the lease), if your mom is the owner (or tenant on the lease), to do so.
Can my step dad steal from my room when I’m gone?
Legally, that isn't permitted. As a practical matter, however, there is no feasible way to enforce those laws in the fact pattern presented by the question.
There are both civil remedies in the form of lawsuits that can be used to recover possession of specific items of personal property or its worth, and criminal penalties for theft.
But, as a practical matter, it is exceedingly unlikely that a lawsuit would provide a cost effective solution, or that the police would intervene in a case like this one.
A lawsuit is a several thousand dollar solution to a several hundred dollar (or less) problem. Also, minors generally need to have some sort of adult guardian or "next friend" to be able to bring a lawsuit. Obtaining this representation would add thousands of dollars of additional cost to the litigation.
The police are overwhelmingly likely to call any such dispute a "family matter" or a "civil matter" and to decline to intervene.
If you are seriously concerned that your stepfather will take items of tangible personal property that belong to you while you are absent from the house, your best practical option is to store those items elsewhere.
On the other hand, if, for example, your stepdad took money from your bank account through unauthorized use of an ATM card or a check book or teller withdrawals from an account where he wasn't an authorized signer or ATM card user, police would be very likely to take that seriously. And, the larger the dollar amount of the transaction, the more viable it would be to enforce your rights.
If your stepdad took property worth $100,000, a lawsuit or criminal charges might be a viable option. At $15,000 it is a close call, but might be possible and might have strategic value to you beyond the net economic recovery you might secure. At $500 of tangible personal property, your formal legal rights are all but irrelevant, and possession in nine-tenths of the law.