My family is renting an apartment on chol hamoed. Presumably, the apartment will be cleaned thoroughly. What are the halachos of kashering the oven, microwave, ect?
However from your question it sounds like you want to perform the kashering on Pesach itself. Any kashering that is based on “haagalah” using heat to extract the chametz flavor from the vessel is ineffective. This includes kashering a microwave, sink, and countertops.
Kashering an oven is done with the “libun” method, destroying the flavor with fire/burning out. While theoretically this may be done on Pesach, it is likely impractical in your setting. An oven will often have residual chametz, crumbs and sometimes more which require cleaning before kashering. This is a very tedious time consuming job, not what people have in mind for Chol Hamoed. If in fact chametz is found it would have to be burnt, another impracticality in a vacation setting.
In fact when you arrive in the apartment on Pesach, if it was not specifically Pesach cleaned [i.e. for chametz such as crumbs etc.] you are required to perform a bedikat chametz when you arrive at the apartment. It may be wise to arrange not to acquire the kitchen appliances so as not to be responsible to clean and check them on Pesach. Any place which may contain chametz should be covered for the duration of Pesach.
See Shulchan Aruch O:C 452:1, 435:1.