Yes, "raid" is OK.
This use of "raid" is common, grammatical (with one issue mentioned below), and natural, in all three sentences in the question that use it. (However,the use of "raiding" here is unlikely unless said while the raid is in progress, or unless there have been a series of raids, as suggested by the comment by FyumbleFingers on the question.) The word "search" could also be used, but it has a somewhat different meaning. A "raid" suggests a sizable police presence, and a threat of force, intended to be sufficiently overwhelming to deter any resistance. It suggests a sudden action without warning. A "search" on the other hand, might be one or two officers with a warrant. Also, a "raid" might be aimed solely or primarily at making arrests, while a search is directed at finding and seizing evidence. Many raids are also searches, and could be described by either term. Sometiems only one term or the other will apply to particular circumstances.
The sentences in the original question do have a problem with number. In my view "The police is raiding their house." should rather be
The police are raiding their house. (treating "the police" as a group)
and "The police has raided their house." should be
The police have raided their house.
On looking at the edit history I see that the question first had the correct forms, and was changed to the incorrect forms "is raiding" and "has raided".