«Сыновья́» is the normal plural.
«Сыны́» sounds archaic or poetic. We don't normally use it to describe the family relations, but use it in different metaphors (e.g. «сыны́ и до́чери Монго́лии» 'sons and daughters of Mongolia' can be a pretentious way to describe Mongolian people). Also, you could use it if you were writing a fantasy novel. :)
(You can compare this usage to the English 'brothers' and 'brethren'. Both are plurals of 'brother', but the first is the normal one, and the second is used metaphorically.)
Having the stressed syllable come last in a multi-syllable word like сыновья is something that I don't believe you find in English, so it's hard (at least for me) to get used to. But that's the way it is, as can be heard in the 5 recordings of сыновья at forvo.com: https://forvo.com/word/%D1%81%D1%8B%D0%BD%D0%BE%D0%B2%D1%8C%D1%8F/#ru
With a word like сыновья, my English-speaking ears want to hear the stress on the 2nd syllable, so it would be сыНОвья, but it's сыновьЯ.