How much grammatically correct is "?!" or "!?" and when to use them?
Most writers use this combination so infrequently that there is no set standard.
There is actually a punctuation mark called the interrobang ("‽") that combines the question mark and the exclamation point. It was invented in1962, and by the end of the decade, some typewriters actually included it on their keyboard. It did not catch on, as few writers preferred it to "?!" or "!?" (which are also called interrobang).
The only time any of these is properly used is in a quote where an angry or excited character is shouting a question. Aside from this answer, I doubt I have used it more than twice in the last 20 years.