similar meaning to "-(て)くれ", but "-(て)おくれ" sounds pretty old and natural only in the imperative form.
"-(て)くれ" makes verb mean like asking a favor to spend his/her time(or something) to do something.
教えてくれ → teach me, please
教えておくれ → teach me, please (but sounds like an old man saying in an old story)
例文:
さあ、夕食を食べておくれ Now is time to have a dinner! (This sounds really like grandmother's saying)
助けておくれ Help me, please. (Must be from old man,,,XD)
NOTE:
"-(て)おくれ" sounds natural only in the imperative form, while "-(て)くれ" is not.
For example,
(彼が)してくれた Thankfully, he did it. (This sounds like "he made an effort to do that")
(彼が)しておくれた : *very unnatural*