(2-part post):
I've caught a bus outside the London Dungeon several times recently and there have always been massive queues for the LD. (I'd guess at an hour long, as a minimum). However there's a separate, shorter queue for visitors with pre-booked tickets. (Even so, you'll still queue for quite some time - perhaps 20 minutes). Once inside, allow about 1½ hours for your visit (although it's easy to go round in far less if you don't take time to study each exhibit).
You simply walk straight in at the Science Museum. There might be a very quick security check (where you're asked to open your bags) but it only delays you for a minute or two at the most. Once you're inside, a quick look round will take you an hour or two. To get the best from the place you need to allow at least 3 hours, but 5 hours would probably be better.
The Natural History Museum is similar to the Science Museum with regards to queues. If you just want to look at the moving dinosaurs and a few other highlights, allow a couple of hours. But you can easily spend 3 or 4 interesting hours there.
Again, you just walk straight in at the V&A. If you're looking at a few selected exhibits (such as the 'Fashion' section and some of the ceramics) allow a couple of hours, but you could easily spend all day in the V&A.
I've not been to the V&A Museum of Childhood. (Indeed, until I read you post and then Googled it, I was unaware that this formerly independent museum now comes under the V&A's umbrella). But I'd expect that you would be able to walk straight in.