Can my landlord rent out a room in my house on Airbnb without my permision?

If that is one of the rooms you are renting--i.e. you leased the entire house, without that room being held back for the landlord's use or otherwise excluded--then no, the landlord may *not* lease it out without your consent or permission. When you lease space, you get exclusive possession to it: the landlord no longer has use of it, and cannot lease it out to anyone else. To do so would be a breach of contract (breach of the lease, which is a contract) and also breach of your right to quiet enjoyment--the landlord's legal obligation to not disturb tenants in their use or possession of the space. If the landlord "rents" out the room, you could deny the renter access to it (you don't need to let him in), call the police on him as a trespasser, consider the lease terminated (over) due to the landlord's breach, and/or sue the landlord for compensation. One thing: if the renter gets in (e.g. the landlord lets him in with another key), do not use force to remove him--call the police and/or run down to the landlord-tenant office of country court and file a legal action (the clerks there can advise you as the one to file and provide instructions on filing it). Only use force against an intruder if you or another person are endangered.
IF that one room was excluded from your rental (i.e. you didn't get use/possession of that room), then the landlord may rent it out.