Webmd says that one way to improve sleep is to:
I want to, but I don’t know how. If we just close the door, the cats will scratch at the door and mew to be left inside. Or they will mew and scratch whenever they want anything. How long before that would dissipate?
One of mine likes sleeping inbetween my legs. I systematically disturb her sleeping position at that location and give her several alternative spots which are attractive to cats.
You have to be consistent with disturbing the cat when it tries to sleep where you don’t want it. You also have to give it something better and accept that kitty is the final arbiter of “better”.
Spray bottle at your night stand. Spray the critters with water every time they jump up onto your bed and say firmly, “Down!”. They won’t persist for very long. A super soaker is another option, which may be over kill… but you did mention that we are talking about cats here…
Also, provide them with their own beds on the floor of your room, since they will probably still want to be nearby. Make sure to be extremely consistent with not allowing them on the bed, and eventually they just won’t come up anymore, preferring to sleep in their own designated beds.
If you’re fine with them being in the room and just want to keep them off the bed, another option after deterring them from the bed itself is to offer acceptable alternatives. Cats often prefer sleeping in elevated places, and soft places, which is why they like the furniture. Cat furniture is your next best bet. Add a nice tall cat tree with 4 or 5 large perches that are comfortable for sleeping. You can also add a cat bed to the top of the dresser or nightstand.
Adding cat trees to the living room and bedroom works in my household because the cats all want to be in the same room as me, so when I go to bed they all follow me in there. They don’t all get along well enough to share the bed with each other, though, and the tree is where they swap space while still hanging out with sleeping me. There’s no squabbling, restlessness, fidgeting, swatting each other, and I get restful sleep without them bothering each other which in turn bothers me.
If the mewing isn’t too loud, maybe you could put something on the door to discourage the scratching. Strips of tape or aluminum foil might work.
With the possible exception of the tag-jiggling, how is this different from sharing the bed with a human?
We had to start using a Sscat Cat Repellent spray to get my cat to stop scratching and mewling at the bedroom door all night, but it works very well for very persistent cats. She just walked over the tape and aluminum we tried first.
I wrapped a 1 x 4 board with rope and nailed it to a wall. The kitty can scratch his little heart out and he won’t ruin my stairs.
I’ve yet to figure out how to keep him out of my room. I don’t really mind the cat. He only stays with me on the bed when the electric blanket is on and even then it’s just for a little while until he wanders off to find some other corner to conk out in.
Now the dog – she’s almost as big as a person, sheds a lot, and is usually filthy. I banned her from the bed and she sleeps in her crate at night, fairly happily. She’d love to be invited upstairs, but she doesn’t whine or cry when I put her to bed in her “office.” Her crate sits partially on top of the heater/ac vent, so it’s warmed or cooled as necessary.
Drew… * Do you like wetting the bed?*
There’s always Scat Mats - you could put one outside your door to deter scratching if all else fails. I haven’t had luck with the repellent sprays, but I’d try that, and other more pleasant alternatives first for sure. But the Scat Mat is a really effective last-resort solution. Bonus: there are lots and lots of fairly hilarious Scat Mat YouTube videos.
Scat Mat has several settings - from a very mild buzz to a harmless, yet definite jolt. I used the latter for The Asshole (Rottweiler), who not only liked to sneak up on the couch when I left the house, but to rip it to shreds. He’s outgrown that now, but the SM effectively deterred him from deconstructing furniture, and I didn’t have to feel like a shit for sticking him a crate all day.
All that said, I don’t mind a cat, or the Small Dog, on my bed. The two big dogs? No. They have comfy dog beds in the bedroom and the Small Dog, being the only female, knows her place and won’t let either of them on the bed. 
Chiroptera, could I attach one of those mats to the door? And would they be on loan or for rent somewhere?
You certainly could attach one to a door. They run off of a single D battery and as long as you don’t stick a push-pin through one of the conduit wires (they’re easy to see), it would be easy.
As far as loaning or renting…I don’t know. The link I provided was for the large SM, they do come in a smaller and cheaper size. I only had to use mine for about a week and the Asshole Rottweiler 
got the message so I have one to spare…but I think mailing one to you could equal the cost of buying a new one (you are in the Netherlands, right?) Otherwise I’d offer to pass it on.
If they’re afraid of the vacuum you could try what a doper in another thread suggested worked for him/her: plug the vacuum into a power strip you can reach from bed. Station vacuum just outside the bedroom door. When they yowl or scratch, lean down and turn it on for 15 seconds. Doesn’t take too long before they associate trying to get into the room with having the crap scared out of them.
Shutting the bedroom door worked with our cat after a couple of nights. She didn’t scratch, though. Earplugs and white noise from an air purifier drowned out the forlorn, uncomprehending cries of sudden abandonment.
I generally find a compressed-air can safer and less messy, while at least as effective.
OTOH, I don’t object to the cat sleeping on the bed with me.
You can teach cats basic stuff like don’t sleep on my bed quite easily. Most people just can be bothered.
Be consistent, enforce simple rules: “don’t be on the table when there’s food”, “don’t mew when we are sleeping” etc. devise some sort of “punishment” that doesn’t hurt them (I clap my hands) and apply it. Expect results in one or two months.
It’s easier to train a positive than a negative. So, instead of trying to train your cat to not sleep on the bed, you aim to train it to sleep somewhere else. It amounts to the same result, but it gives you a positive behavior to work towards.
As the other posters have mentioned, you should decide where you DO want them to sleep - in your room or outside it? Using the physical barrier of the bedroom door is certainly an easy way of avoiding the unwanted behavior (sleeping on your bed) - but, as you mention, is likely to be replaced with other unwanted behaviors (scratching/mewing at the door).
Appeal to cat instincts, which can vary by individual. A wall shelf with a cat bed might be easy and cheap to install, and appeal to your pets.
Since I’m deaf as a doorpost when I’m asleep (and find it incredibly easy to ignore sounds when I’m not), we just keep our bedroom door closed.
Put a basket of freshly washed and folded laundry in the room somewhere. Cats are attracted to clean laundry like it is made of cat food and happiness.
If you REALLY don’t want a pet on your bed when you sleep, your best bet is to train the pet YOUNG. As soon as you bring the beast into your home, start teaching that the bed is verboten.
As for me, my kitty had to go to the vet today. He’s Diabetic, and stopped eating for the past two days. He had a full blood panel workup, and his insulin/sugar ratios are off, plus he’s got an infection. He had to stay at the vet’s for IV therapy.
I’m gonna miss him tonight on my bed.
~VOW