**і**

- If sound is not alone in syllabe like in *піт*, *вирій* then it is [i] like in English [key](https://dictionary.cambridge.org/dictionary/english/key) [kiː], [keep](https://dictionary.cambridge.org/dictionary/english/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](https://en.wikipedia.org/wiki/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](https://r2u.org.ua/guides/synyavsky/ortoepia).