I have heard the word fuckstick in a lot of Hollywood movies, most notably in 'The Shawshank Redemption'.
What is this word even meant to convey? An insult? Is it even abusive? Or is just a combination of two random words?
I wonder if the stick part could have been chosen by analogy with dipstick, which was used as a mild insult starting in the 1920s. (Of course, "Shawshank Redemption" isn't really from that time period, but was written recently by Stephen King, so even if someone from the 1920s wouldn't really have said that, it wouldn't invalidate the theory.) There is no way to really know for sure, unless we ask King himself; and even he might not consciously know why he chose that.
Dipstick can still be used today, but remains very mild as far as insults go. Changing dip to fuck would take that mild insult and make it into something much more offensive. I have certainly heard fuckstick before, but it isn't particularly common compared to other similar insults.
I have to say, as an English speaker, I find it to be one of the more amusing insult constructions involving the word fuck (because it is almost silly), but if said in the right manner by someone in the right situation, could still make the name-receiver quite quite angry and insulted.
As mentioned by Martha, a fuckstick could also be interpreted as a dildo, or something with this sort of sexual connotation.