Alphabetical Syntagma
αιτιώματα, "accusations," is an exceedingly rare word. Blass still considered it a hapax, saying: "αιτίωμα pro αιτίαμα nusquam extat." The only example of its use known to me, apart from this passage, is found in P.Fay. 111.8, from A.D. 95/96.
ούκισχυον, "they had no strength," is an imperfect tense and implies many unsuccessful attempts. Barrett thinks that, in principle, it could be translated: "They could not prove it, however hard they tried."
The scene is described very summarily. The contents of the accusations are not reported, though the reader already knows them; see the commentary on Acts 24:5. Yet Paul's answer, also very brief, shows that they had not changed; see the commentary on Acts 25:8.