To carry/hide something, usually in an illegal situation such as hiding contraband items when being taken into custody or smuggling them past initial inspection when being admitted to rehab.
Item being 'stuked' would be something useful or valuable to you in this situation such as drugs, money or cigarettes. It could however, be a sentimental item such as a photo or jewellery containing inscriptions or a locket with a photograph.
You could also stuke something like money from an armed robbery or even every day items that you didn't want someone in particular to find.
ie: "have you got any stukies?" or "Where'd ya stuke that dope I got you to hold?" or "I stuked it in your pillow case".
1) As you're being taken to jail or holding cells, you quickly and subtley remove your jewellery, cash & drugs and place them into a container which you then stick up any orifice of your choice.
2) You spot your mistress's bra that she's left behind on your couch, just as you hear you're wife's car pull into the driveway, so you quickly stuke the bra behind the fridge where your wife won't see it.