When it comes to timetable it's always better to check official websites of national railways you plan to use (
Hungarian,
Romanian etc.) or alternatively
DB website, which almost always have the same info. Regarding your question, Budapest-Oradea by train takes from 4,5 to 5,5 hours depending on connection, while Oradea-Athens is much longer + not really possible, since Greek railways ceased all the international passenger rail connection to/from Greece, so you simply can't cross the Greek border on train. Although you can first travel Oreadea-Sofia (22+ hours with at least one change), then take a bus from Sofia to Thessaloniki (roughly another 6 hours) and finally train again from Thessaloniki to Athens (5:15-6 hours depending on connection)
Regarding fares and tickets, Budapest-Oradea ticket standard price (when purchasing in Hungary) is 18,2 euro, and that is basically the best you can do (in case you keep everything legal), with Oradea-Athens there are a lot of factors, but probably best solution isn't going with direct point-to-point tickets, but instead with Balkan Flexi Pass (more on that on our country pages). Plus such pass will allow you more flexibility, regarding various detours and additional travels in the region
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