Advice on cat who urinates outside litter box

Hi all,
I have a question about my cats urinating outside the litter box. I'm
hoping someone here might have some advice. I'll try to give as much
details as possible, but if you need to know more please ask.

I have three cats. Two of them I got on the same day from the same
place (not biological sisters) in Nov 2001 when they were no older than
7-8 weeks old. The third one was rescued in July 2002 when she was
about 6-7 weeks old. The resuced cat was traumatized when we think she
was about five weeks old (six at the latest). We think she was hit by
a car (that's a WHOLE different story). One of the other two is
epileptic, though the cause is unknown. The third seems to be totally
fine.

I scoop their box daily. They have plenty of litter in it. But for a
while now occasionally one of them (well, who knows... could be all of
them rotating, I wouldn't know) urinates in my closet. It has always
been contained to my dirty clothes basket. Last week I noticed that
someone had urinated on a pair of sneakers I had on the floor by the
basket. Tonight I just discovered someone urinated on a pile of
clothes that are on a shelf at a minimum of four feet up (probably
closer to five feet). **This is the first time something like this has
ever happened**

Obviously this is a problem. An immediate response I have is to close
them off to my bedroom whenever I'm not here (no matter how long I'm
gone). BUT, of course this won't stop them if I'm downstairs and in
the house, or if I'm at work, or even when I'm asleep. This is clearly
becoming a problem. I don't think it's possible or even kind (for lack
of a better word) for me to close them off from the bedroom at all
other times. BUHLIEVE ME! I've tried to sleep with the door closed
(they take up so much of the bed :-) but they literally fling their
bodies up against the door -- I know, because someone outside the door
witnessed it. So, that's not really an option. If I close the door
even when I'm home then I'd feel like I'm really alienating them. They
hang in my room when I'm not here because it's *my* room.

Another thing I've thought of is setting up a webcam to surveil the
closet. I swear, I'd watch the footage - minute by minute - to figure
this out. I'm hoping to see that it's only one of them and then take
her to the vet to have her checked out.

So, I have questions. Is this behavioral? Is it medical? Is it just
one of them marking her territory, or could it be more than one of
them? Is there something else I should do?

I'm absolutely committed to giving them the best life possible. The
four of us are very tight: whenever I'm home the three of them stick to
me like white on rice! But something's wrong and I want to figure it
out. I thought I'd ask you to see if you can help!

Thanks so much!