Housekeeping is not my department but ill try and write the way I deal with my microwave
First of all, try not dirtying the microwave at all. Believe me, spend 15 seconds extra and cover up whatever you are trying to heat up especially items with oil - cover them up with a plate or the Microwave covers you get in the market.
This would help you a lot when it comes to cleaning your microwave as you will not have to fight with tough Oil Stains. I used to be slack and never covered my food items while heating them up. But at the end of the month, I paid for it. Had to fight with it.
I normally use WinDex liquid to clean my oven. You can use any liquid I guess - it dosent matter. Problem with Windex was that it smells of Ammonia - so I wasnt that happy after using it. But it cleaned well.
The imprtant thing is that after you have cleaned the oven, you should not use it immediately and leave it to dry for a while. I do not think there are any problems with using liquids - infact they work the best!