The vacuum of space is only -14.7 psi compared to normal air. You probably wouldn't want to vacation there, but it's not enough to explode you Hollywood style.
Medical oxygen tanks are pressurized up to 2200 psi. That's 150 times greater pressure difference than inside your body and the vacuum of space. Obviously, human bodies aren't as strong as oxygen tanks, but the same principle applies.
It's not about the pressure difference between inside and out. It's about the internal pressure overpowering the vessel it's in. As long as your skin and blood vessels don't break, the oxygen has nowhere to go. (Of course, the strain on your skin and blood vessels is related to that pressure difference, but there's just not enough to tear through most places on your body.)
For the same reasons, your blood pressure won't change unless something ruptures. It's likely you get some capillaries near the surface that do rupture, but they're so tiny the blood in your body can't escape very quickly. I'd guess your body would stop the bleeding before your blood loss was high enough to substantially alter blood pressure, but I've never tried it.
Now, if your lungs are exposed, things change. We're designed to work at normal atmospheric pressure. In a vacuum, the blood/lung interface will likely allow bodily fluids to boil out, but you'll probably pass out and die from the lack of oxygen before your blood boils out substantially.
Similarly, your sweat glands will start dehydrating you, because space is extremely dry. But your body isn't an open system, so it won't instantly suck all the moisture out of your body.
Also, I'm guessing your ears, nose, tear ducts, etc. won't like you after your sojourn to space if you leave them unprotected, but I'm not sure how much actual damage would be done. The air pressure inside your eardrums would evacuate via the Eustachian tube, but the tube is normally closed by muscles in the back of the throat. It's possible the pressure could rupture your eardrum before the pressurized air forced its way through your throat.
Your bowels and bladder would tend to empty themselves, and the extra pressure might be too much for the usual protections to function, but I'm not sure. The same problem would happen at the other end, and you might well end up with your lunch flying off into space.
Space itself has no temperature, but you're still bound by blackbody radiation. The ~2.7 K microwave radiation isn't enough to keep you warm, so you'd freeze to death as your body heat evaporates and radiates out of you without nearby heat sources. And something like the 6000 K radiation from the sun would burn you alive if you were too close, because you couldn't remove heat fast enough.
Also, I'm sure you'll end up with some nasty skin problems with how dry space is. The longer you're up there, the worse the problems will get.
With a spacesuit on, the pressure differences are placed on the suit, rather than your sensitive bits, so you can remain comfortable indefinitely. Additionally, spacesuits have oxygen tanks and are designed to keep you at a decent temperature.