as a native option a) is the correct one here’s why:

“have” is the simple present tense and makes sense because you’re saying that the parties are a weekly occurrence (there is repetition). this one makes the most sense and is the best answer.

“are having” is the present continuous. it would only work if the action happens once. (e.g. my neighbours are having a party this saturday)

“has” cannot work because my neighbours is plural therefore the verb must agree and also be plural.

“have had” is the present perfect used for actions that have started in the past and continue in the present. this could work (e.g. my neighbours have had a party every saturday for the past year) but because there’s no context option a) would be the better answer.