「訳す」 and 「訳する」 have the same meanings.
A) To translate a foreign language into Japanese.
B)To translate Japanese classics into modern Japanese.
「訳す」 is a literary style and 「訳する」 is a colloquial style and conjugate in different ways.
「翻訳する」 generally has the usage of A) only.
「通訳する」 means to interpret a foreign language orally and 「翻訳する」「訳す」「訳する」 mean to translate a written language. But you can use 「翻訳する」 to translate cultures and code or sign.
In colloquial use, you may ask your friend to interpret conversations saying 「訳してくれない?」
I myself use 「訳す」 more often than 「訳する」 even in colloquial use. Sounds natural to me.
And if you want to ask somebody politely to translate English to Japanese, you should say 「英語から日本語へ翻訳してくれませんか?」which is clearer as well as politer.