Hath been taken (kateilēptai). Perfect passive indicative of katalambanō (see Joh 8:3), caught and still guilty.
In adultery (moicheuomenē). Present passive participle of moicheuō, “herself suffering adultery” (Mat 5:32). Used of married people. Not in John.
In the very act (ep' autophōrōi). Old adjective (autophōros, autos, self, and phōr, thief) caught in the act of theft, then extended to any crime in which one is caught. Old idiom, but not elsewhere in the Greek Bible. One example in a Berlin papyrus.