If only writers would dump the mixing up of these three words into File 13!

Threw is the easy word to distinguish among these three. It means to toss, as in A movie star threw the baseball season’s opening pitch or He threw away the old papers.

Through means to go in one side and come out the other, as in They drove through a long mountain tunnel.

Thru is an informal, simplified spelling of through. So you technically would be correct to write They drove thru a long mountain tunnel.

As an informal word, thru is probably fine in emails, texts and letters to friends, but in academic papers, book manuscripts and business communication, you’d want to use through.