While oddly enough is used most often to introduce something that is counterintuitive (and much less often in an ironic sense), I have only very rarely heard or seen shockingly enough used outside of a context similar to this:
Shockingly enough, Albanian is spoken mostly in Albania.
That use can be described as "ironic" in much the same way as a TI class supertanker can be described as "sort of a large canoe". Far from indicating any degree of shock, the phrase is most often used to point out the blindingly obvious.
That is not to say that it is never used in a literal sense. When it is used without irony, it is not usually an understatement:
Shockingly enough, most of the actual violence is carried out by school-age children and not by the veterans of the gang because of laws limiting the sentences of juvenile offenders.
In both phrases, enough is probably superfluous, but it is idiomatic, particularly when the phrase is used ironically.