I understand that ~てください is the polite request form, and that both ~てくれ and simply using the ~て form are both more colloquial. I'm just not sure how they compare, my guess would be that ~てくれ is more rough, but I'm not sure.
1 Answer
In the case of making requests, て on its own is just a shortened version of てください which isn't that much more informal than ~てください. ~てくれ is using the imperative form of くれる which is much more forward and commanding than ください or て. So, your intuition is spot on. A more polite way of てくれ would be something like ~てくれないか or ~てくれませんか.