Oops, my mistake, it isn't a diphthong its a double consonant (which I always confuse with diphthongs), but unless there is an exception it is supposed to be pronounced like ng, or at least that's how I've heard native Greek speakers pronounce it, but that may just be a regional difference, I'm not quite sure. Do you know by any chance?
Αγγίζω is more like touching with your fingers and sensing. Ακουμπάω is just touching ie putting a part of your body on it. Ακουμπάω can also mean put,place (temporarily, for a while). P.e. "I touch it and it is soft-το άγγιζω και είναι μαλακό", "I did not hit you! I just touched you!-δεν σε χτύπησα! Μόλις που σε ακούμπησα", "I put the cake on the table (for a while) - ακούμπησα το κέικ στο τραπέζι." You can use one in place of the other (except in the meaning of put), though.