"Matěj and his brother are my uncles."

Translation: Matěj a jeho bratr jsou moji strýci.

[DaanBanaan18]

Which is the most commonly used? Strýci or strýcové?

[endless_sleeper]

'Strýcové', at least according to the Czech language corpus.

[yoelchico]

Would strýcům be correct?

[endless_sleeper]

No. 'Strýcům' is dative plural, you need nominative here.