I have a lot of U2 vinyl, from the old stuff to the new stuff. The most recent 45 rpm single I was able to find was "Discotheque." So yes, labels still make some 45 rpm singles - even in '97. I also have the album version of ATYCLB, so companies are clearly still releasing vinyl.
Having collected albums since the 70's (arguably the very end of the 60's, when my mother bought the Beatles' "Let It Be" for me as a child), I have a fair amount of vinyl (most of it not that great - a lot of typical male teenage crap) and a turntable. Turntables are fairly cheap these days, so if you do want to play your albums, it shouldn't cost too much to get one.
Regarding the singles you mentioned ~LadyLemon~, I don't have "Stay" (so if you find an extra one, let me know) but I have "Desire." I bought that one when it was released and I have since acquired a few more copies. Both singles are pretty much worth what you paid for them at the moment. I would estimate about $2-5. You might find someone willing to pay more, say $10, but that's about it. If they are in their special sleeves, they are (will be) worth more than if they are in plain sleeves.
As someone else mentioned, the singles worth a lot right now are the "much older" ones released early in U2's career. Just about any version of "U2-3" for example is fairly valuable. An original "U2-3" (the 12" version which has a number) is worth as much as $1500! However, I believe it will take another 10 or so years before most of U2's vinyl really starts becoming valuable.
There are two exceptions, from my experience, of more recent U2 45 rpm vinyl singles that are more valuable. One is "One Tree Hill." This record was only released in New Zealand. Its sleeve looks just like the one for "In God's Country" (with a picture of Bono on it) but comes with a special lyric sheet. That lyric sheet is part of what makes this 45 rpm valuable, so don't lose it. That single can go for as high as $50 due to its rather limited release (worth much less without the lyric sheet). The other is a gatefold version of "Desire." By "gatefold" I mean that the record cover folds out. That is worth about $15-20. Most of the other singles are worth $10 and under ($10 is the maximum price I've seen for singles - don't be tempted to pay it unless you absolutely can't find it elsewhere - try not to pay more than $5 for a typical vinyl single).
Hope this helps.
