Asseverative ἦ (prepositive) in truth, in sooth, verily, upon my honour, etc.; as ἦ καλῶς λέγεις
ἦ is usually associated with other particles.
ἦ γάρ when used alone in dialogue =
ἦ δή expresses lively surprise.
ἦ καί is found in animated questions. Here καί goes closely with ἦ.
ἦ μήν (Hom. ἦ μέν, ἦ μά_ν) prefaces strong asseverations, threats, and oaths, in direct and indirect discourse. Thus,
ἦ μὴν ἐγὼ ἔπαθόν τι τοιοῦτον
ὄμνυ_μι θεοὺς . . . ἦ μὴν μήτε με Ξενοφῶντα κελεῦσαι ἀφελέσθαι τὸν ἄνδρα μήτε ἄλλον ὑ_μῶν μηδένα
Interrogative ἦ ( cross2650) is probably the same as asseverative ἦ.
Herbert Weir Smyth [n.d.], A Greek Grammar for Colleges; Machine readable text [info] [word count] [Smyth].