What is the ruling on praying the Sunnah of 'Isha' if the worshipper catches the Imam while he is praying Tarawih, and what is the ruling on someone who catches the Imam in the last rak'ah of Witr, should he join him or has he missed the reward?

If a Muslim enters the mosque and finds the Tarawih congregation but has not prayed Isha, he should join them with the intention of praying Isha. When the Imam says the taslim (concludes the prayer), he should stand up and complete his prayer. After that, he can join them again with the intention of praying the regular Sunnah prayer (ratibat al-Isha).

As for the Witr prayer with the Imam for someone who wishes to pray after him, if he misses the bowing (ruku') with the Imam in Witr, then he has missed praying Witr with the Imam.