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.
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.