I think the answer to the riddle is:
RECURSION
Look for the infix, odious indeed,
Obscenities and evil, a hex, but no e.
The infix is CURS - the word CURSE (which can mean both 'obscenity' and 'hex') without the 'E'.
Oddly the suffix, denotes with just three,
The suffix is ION - this is a 3-letter acronym for 'In Other News', the phrase sometimes spoken in news broadcasts just before the 'odd' ('oddly') or novelty news item at the end of the bulletin...
Prefixed by back, again, it is ?
The prefix is RE, as in 'repeat', meaning 'back, again'... Note that this word completes the rhyme here:
Oddly the suffix, denotes with just three,
Prefixed by back, again, it is RE
As for the title:
Tree recursion is a programming term related to looping repetitions in code. Note also that the first letters of each line spell the word 'LOOP' - we've come full circle!