I try to use a credit card for everything, to improve my credit score (as I moved to the US only last year). However, my landlord only accepts wire transfers. I know I can get money off my card and use that, but AFAIK that accrues very high interest immediately. Is there any online service that lets you pay them with a credit card (as a purchase) and they make a deposit for you?
There may be such services, but it will be treated the exact same way as regular cash advance: accrue very high interest immediately.
Credit cards are good for purchases, not payments. You cannot treat credit card as a source of cash, since it is very expensive. The reason it is so expensive is twofold:
It is a very high risk for the credit card company, since you're getting cash and can just disappear on them (products are less risky since you're not getting cash into your hand and they may find you and recover their money buy forcing you to sell whatever that was that you bought).
People who take cash out of their credit cards are usually desperate for cash and have no other choice, and will pay whatever. Or ignorant, and will pay whatever. Ignorants provide easy source of income to the credit card companies, while the desperates are the source of the risk and losses.