What are some examples of awkward sounding but grammatically correct sentences?
As far as awkward-sounding is concerned, I submit there are few sentences spoken in English that sound more awkward than:
Ed had edited it.
This is very hard to say in the rapid flow of conversation, and results in a sound something like:
Try it for yourself, speaking quickly, and you'll see what I mean.
Ending a sentence with a preposition is something up with which we will not put.
— Someone who was not Winston Churchill
How about some semantic awkwardness?
"Colorless green ideas sleep furiously" —Noam Chomsky
You'll probably want to put some punctuation in these:
Wouldn't the sentence "I want to put a hyphen between the words Fish and and and and and Chips in my 'Fish and Chips' sign" have been clearer if quotation marks had been placed before Fish, and between Fish and and, and and and and, and and and and, and and and and, and and and and, and and and Chips, as well as after Chips?
James while John had had had had had had had had had had had a better effect on the teacher.