Both "서혜부" and "사타구니" mean the same thing in English, "groin". Personally, I wouldn't consider "서혜부" an everyday word, though it is used frequently. I'd say, "서혜부" is a more medical/anatomic term vis-à-vis "사타구니", which could be more commonly used in a day-to-day converstaion.
In a literal sense, "가랑이" refers to our limbs that diverge from our body, split/forked into two, just like our legs. If you look it up in a dictionary, "가랑이" is translated as "crotch", and its synonym is interestingly "legs" rather than "groin". However, keep in mind that the emphasis here when using the term "가랑이" is that juncture, the crotch region where legs open and close, not the legs themselves.
"샅" refers to a more specific region of one's body and is much wider than the groin or crotch area: inner thigh. It is translated as the region between one's thighs and sex organ. In fact, the aforementioned "사타구니" originates from the term, "샅": it is a combination of "샅" and "아구니", which is a familiar native Korean term meaning a "gap" or a "crack". (It makes sense if you take into account where each of the terms "사타구니" and "샅" refers to.)
Hope this helps!
I'd say "샅" extends all the way up to the crotch region as I've specified in the previous comment: it is translated as the region between one's thighs and sex organ.
Also, "가랑이" refers to both junctures where our legs start, diverge from our body and fork into two. Hope this clarifies.