"Do you have a radio or a television?"
Translation:Onko sinulla radiota tai televisiota?
'Tai' is used if both can be true and 'vai' is used if only other can be true. https://uusikielemme.fi/finnish-vocabulary/interesting-words/the-difference-between-tai-and-vai/
You can use nominative and ask "Onko sinulla radio tai televisio?" but then it also sounds more like one must be true (and that you have exactly one radio or television) because using the nominative makes it sound more definite, like you are talking about a specific brand, model etc. The partitive doesn't assume anything. You might have a radio - or not. You might have a television - or not.
It is impossible to tell from the English context whether "tai" or "vai" is correct in this sentence.
The English sentence could mean "Which of these do you have: a radio or a television?" In which case, "vai" would be correct because the answer must be either "a radio" or "a television".
Or it could mean "Do you have any of these things: a radio, a television?" In which case, "tai" would be correct because the answer could be "a radio", "a television", "both", or "neither".