Woe to them (ouai autois). Interjection with the dative as is common in the Gospels (Mat 11:21).
Went (eporeuthēsan). First aorist passive (deponent) indicative of poreuomai.
In the way of Cain (tēi hodōi tou Kain). Locative case hodōi. Cain is Jude’s fourth example. Not in 2 Peter, but in Heb 11:4; 1Jo 3:11. From Gen 4:7.
Ran riotously (exechuthēsan). First aorist passive indicative of ekcheō, to pour out, “they were poured out,” vigorous metaphor for excessive indulgence. But it is used also of God’s love for us (Rom 5:5).
In the error of Balaam (tēi planēi tou Balaam). The fifth example in Jude. In 2 Peter also (2Pe 2:15). Either locative case (in) or instrumental (by). Planē (in Peter also) is the common word for such wandering (Mat 24:4., etc.).
Perished (apōlonto). Second aorist middle (intransitive) of apollumi.
In the gainsaying of Korah (tēi antilogiāi tou Kore). Again either locative or instrumental. The word antilogia is originally answering back (Heb 6:16), but it may be by act also (Rom 10:21) as here. This is the sixth example in Jude, not in 2 Peter.