і
- If sound is not alone in syllabe like in піт, вирій then it is [i] like in English key [kiː], keep [kiːp] but shorter.
- If alone in syllabe and next sound is not н or р like Іван, імовірно, іти then it can be a semivowel і aka [i̯]. It is shorter than common і. That why mentioned words can be writed also as Йван, ймовірно, йти.
- Same but next sound is н or р like інший, ірод then it is и. That why mentioned words can be writed also as инший, ирод.
й
- If vowel after й and they are in the same syllabe like in йод, Йосип then it is [j] like in English yield [jiːld], yo-yo [joʊ.joʊ]. For example найочевидніша is out this rule because й and о are not in the same syllabe.
- In other cases it is a just [i̯].
и
- If stressed then it is like English [six].(https://dictionary.cambridge.org/dictionary/english/six) [sɪks]
- If not then it can be sound close to unsressed e. Yeah, мене and мине are very similar even for Ukrainian and it is popular mistake when someone write write е instead и or back way.
So in result do we have ий as [ɪi̯] (бий) or [ɪj] (прийом)? Yes.
And ій as [ii̯] (бій) or [ij] (ійон)? Well, yes, but actually not always.
In some cases i it is just „soft” и aka ьи which it is [ʲɪ]. It is not so hard cause you need just compare with „hard” и. It is always for all adjective: синій ['sɪnʲɪi̯] which is from синь [sɪnʲ], and we have „hard” in червоний [t͡ʃer'ʋɔnɪi̯]. That is why ій and ий can sound simillar for author of question.
Source. Олекса Синявський. Норми української мови, ортоепія.