Both of the above answers are good and they follow an important general rule: don't mix tenses. However, because you use the conjunction "so", both 1) and 2) can be correct. IF you had said ''At first I thought he was 16, and then all of a sudden he told me he is 20 *AND* I WAS like, what?!'', then "WAS" is correct because all three events happened in the past. But since you used the conjunction "so", you can separate out the two first events and the third: ''At first I thought he was 16, and then all of a sudden he told me he is 20" - those happened in the past. "so..." then adds a state that could be in the past or in the present. "so (now) I am like what?!" - means that you still feel that way, you're still confused about what happened, your current feeling is ongoing. "so (then) I was like what?!" - means, at that time, you were confused and befuddled, but not necessarily anymore. I hope that distinction makes sense.

i think it depends on the kind of quotation you are using if you use direct quotation it will like (At first I thought he was 16, and then all of a sudden he told " i am 20" so I WAS like, what?!) and if you use indirect quotation it will be like (At first I thought he was 16, and then all of a sudden he told me (that) he was 20 so I WAS like, what?!) you have to use the tense consistently,

The second sentence is more correct, but there is still a mistake ''At first I thought he was 16, and then all of a sudden he told me he WAS 20 so I was like, what?!'' You should always use past tense consistently, without mixing in present. If you were citing him, it could become: ''At first I thought he was 16, and then all of a sudden he told me: "I am 20" so I was like, what?!''