While super- and hyper- have approximately the same meanings, they are not interchangeable, in that for a particular X, it will be either superX or hyperX that gets established, and the other one is never seen. There is usually no deep reason why one rather than the other gets established, and if one is in the position of coining a new term of that kind, one is generally free to choose either superX or hyperX. In some contexts, both may be used as technical terms with different meanings, but in such cases their different meanings have to be explicitly stipulated; it won't be possible to deduce them from the meanings of the prefixes themselves.
One limitation on superX, though, is that it is normally not used in the cases in which exceeding the standard limits of X is undesirable. HyperX, on the other hand, may be used in such cases as well, which is why it often appears in medical contexts, in the names of abnormal conditions.
Unlike super- and hyper-, which have a long history as components of everyday English, meta- is a prefix that has its proper use only in relatively specialised vocabularies. (It now seems to have started to percolate into colloquial English, but its meaning in such contexts is unsettled.) Somebody who is not familiar with the actual use of meta-, but is just given its short dictionary definition of the sort that is quoted by the OP, may be under an impression that its meaning is similar to that of super- and hyper-, but the similarity of the definitions is superficial and misleading. MetaX is something that is about X; that is above X only in a highly metaphorical sense of above. Metadata, for example, are data that are about other data, and that puts them above these other data, but in a much more metaphorical sense, than the sense in which supersonic speeds are above the speed of sound.
Mind the poor formatting.
– Marquise Sep 01 '20 at 13:07