A pair of definitions I find useful:
Verb. 1. to spend the night as a guest in someone's home
Noun. 1. the act of spending the night as a guest in another's house, especially the participants are children
As you can see, sleep over and/or sleepover have two related meanings, one as a verb and one as a noun.
To sleep over does not necessarily imply that children are involved, but it can imply a certain innocence. (It also sometimes does not.) Paired with the discussion of the couch, the phrase indicates that Jerry is not talking about anyone who would share his bed.
Rather, Jerry is talking about guests who are overstaying their welcome. Much of Seinfeld is about parodying awkward social situations. This is one such case.
Before getting the new couch, Jerry had a couch that could fold out into a bed. This meant that, in addition to his own bed, there was a second bed not normally in use. Guests could use it to spend the night, that is, to sleep over. Jerry simply does not want to have guests over all night, but also does not want to be seen as rude in denying them the option of using the bed. (Note that it would be extremely presumptuous to assume you are welcome to use someone's bed, even a guest bed, but then Seinfeld characters are often rude and presumptuous. It's still awkward to inform someone that they presume too much and are not, in fact, welcome to use the bed.)
The new couch does not fold out into a bed, so there is nowhere for a guest to sleep (sleeping on a couch tends to be uncomfortable). This gives Jerry the perfect excuse to stop people from sleeping over, without having to be seen as rude. This is a pretty typical Seinfeld joke, parodying rules of manners and politeness, particularly with characters who are not actually all that polite, but try to act it.
So the joke is that, rather than things like comfort or utility or even its decorative properties, the thing Jerry likes best about the couch is that he can avoid this awkward situation. In fact, the ability to fold out into a bed is usually seen as a feature, so the thing he likes most about the bed is its lack of a feature that others might pay extra for. As jokes go, its not exactly hilarious, but it is mildly humorous and is part of the way Seinfeld constantly reinforces its characters' personalities and exhibits their often-skewed priorities.
The option of sleeping in Jerry's bed isn't part of the joke. Unless the guest is a close childhood friend or relative, the very phrase sharing a bed often implies sex. Sharing a bed is very intimate, even when not sexually intimate. None of Jerry's unwanted guests would be that intimate with him (or at least, so he believes; I don't remember if it happened at any point, but it would be a very Seinfeld-like joke to have one of the unwanted guests suggest it, flustering Jerry and putting him in an even more awkward situation).