I'm sure I'll catch heck for this, but I really bet it is not the twine knives. They just don't have to be that sharp to tie properly, and if they were that dull, you'd have really fraid twine ends, or maybe not cutting it at all.
You say you're just forking straw into the baler. How tight are the bales coming out? Without a decent amount of tension, that can be a common problem. When I start the balers empty every spring, they will almost always hang up on the bill hook till you get a solid bale in the chamber. If you are making decent bales (desity wise), is the knot just hung in the billhook, or is the twine wrapped around the billhook? If it's just hung up, in the billhook jaws, then I'd bet on too much billhook tension, insufficent wiper arm travel, or your wiper not running tight enough to the billhook. If the twine is wrapped around the billhook, then I'd kind of guess tucker fingers out of adjustment, but there are others.