1. He vomited all the cookies he had eaten.

2. He vomited all the cookies he ate.

3. She was not so beautiful as I had imagined.

4. She was not so beautiful as I imagined.

(Which ones are correct? Do we have to use the past tense or the past participle tense? Are all correct? Then, what is the difference?)

#1 is better than #2 because of the sequence of tenses.

#3 is better than #4 for the same reason. Also in #s 3 and 4, I'd say "...not as beautiful as ... "