ἀλλὰ τούτων μὲν τάχ᾽ ἡμῖν δώσετον καλὴν δίκην,
οὐκέτ᾽ ἐς μακρὰν ἵν᾽ εἰδῆθ᾽ οἷός ἐστ᾽ ἀνδρῶν τρόπος
ὀξυθύμων καὶ δικαίων καὶ βλεπόντων κάρδαμα.
lit: ‘So that you know of what sort is the character of men who are hot-tempered and…’
I’m not entirely sure why ‘οἱος…τροπος’ isn’t accusative - isn’t it the object of εἰδητε? The commentary I’m reading says it shouldn’t be the acc object of εἰδητε but doesn’t go on to explain why. I would be grateful if anyone could explain!
It modifies the subject of ἐστί and that throws it into the nominative. We do something similar in English:
“I know who wrote the book” not “I know whom wrote the book.” Although the entire clause is the object of “know” we put the “who” in the subject case. Also in Greek – subordinate relatives and indirect question words go into the case required by their use in the clause.
This is an indirect question. It’s a subordinate clause with its own verb, and οἱος…τροπος is the subject.
Thank you both for your help 
“I know what you’re like” = οιδα (σε) οἷος εἶ (I know of what sort you are)
“You’re the sort of person I like” = τοιοῦτος εἶ οἷον φιλῶ. (correlatives)