Wow so many options. Aside from basic ideas like board games, imaginative stuff, puzzles, artsy coloring stuff… I'm just naming general topics but a quick Google search with "ideas" or put those age ranges in should help.
First set - you may have problems with them trying to "play together". Those are all ages where the kids are very different, and the 10 year old will be too "cool" for the 5, the 2 may have tantrums still that the 5 & 10 don't like… Etc. I'd say try to engage them or maybe have the 10 year old help you "teach" something to the younger ones, or give him a leader type of role. That would probably help him stay engaged if you're trying to do something as group.
2nd -- this is the one that caught my eye. If it's still too cold for outside, engaging in the Lego stuff is fine. Be prepared to learn about Minecraft… My brother who's 11 and many other kids in this age range are getting addicted to this stuff -- and it's not all bad. It's a fun world. If he's going outside to play, it very well may take the form of some kind of imaginative Minecraft setting. Or hey maybe he loves hitting whiffleballs but just doesn't have anyone to do it with. It depends on the kid -- but minecraft ISN'T inherently bad. I'd definitely suggest embracing it cause kids can learn a LOT of cool stuff from it.
3rd - obviously the 4 month old doesn't really need "games", any kind of engaging materials, blocks, rattles, etc. Will work. Kind of ditto with the 1.5, just read to him, get silly, go over young learning toys. Again the possibilities are kind of endless.
Sorry if some of it's vague, but as long as you have the mindset of "exploring" the world, or whatever materials or toys they have at the house, the kids will get along just fine.
