I second the vote for the humidifier. It can really help.
A few suggestions - get all your friends together and tell them to bring their lotions, creams, and other moisturizing potions. Have a lotion party. Roll up your pants legs and start sampling. See which products feel best on your skin. (While you're at it, read labels for any ingredients you want to avoid.)
Also, many health food stores have sample bottles of products on their shelves - or ask the owner if they have samples - rub them on your arms, and see how they feel. You're right that lotions can be expensive, and I don't think you should be afraid of asking to try them before you sink money into them. Also, I'm no lotion expert, but I've found that people who run health food stores usually know a lot about their products - ask them for a recommendation, but also ask for a sample, or tell them you're 'just looking' if they start to pressure you to buy something. (What I'm trying to say is, if they point to the most expensive lotion on the shelf, don't feel obligated to buy it. I once had a not-nice health food store owner push some expensive and useless stuff on me, which I bought like an idiot.)
In the past, I have found that lotions made primarily with cocoa butter are very effective, although you might not like the chocolatey smell. Shea butter products are also very good. I understand that you don't like the feeling of lotion on your legs, but I really don't think there's much of a way around that. For me, I just deal with that unpleasantness - it's much better than dealing with the itchy skin.
I have not found any moisturizing body wash that allows me to skip applying lotion after I shower. I get out of the shower, towel off, and immediately slather up my legs with lotion. There's just no way around that, for me. (Otherwise, my skin gets so itchy that I will scratch it until it bleeds or looks like it's covered in welts.)
For your hands, I would recommend getting a cheap pair of cotton gloves. (Sometimes you can find these in stores near the lotions.) Before bed, lotion your hands, then put on the gloves. That will help you get the maximum benefit from the lotion overnight. (Or, you could put socks on your hands, like mittens. That works too. It just keeps the lotion from drying too quickly or rubbing off while you sleep.)
For the face, in the winter I use whatever heavy-duty body moisturizer I'm using on my body. I have never found a face lotion that was able to keep my face moisturized in the winter. (Most face lotions are too thin in consistency, and it feels like they just sit on the surface of the skin. Body moisturizers are much thicker. In the morning, you could wash your face, put on moisturizer, then go eat breakfast or something while you wait for the lotion to thoroughly sink in - then apply makeup, if that's what you do.)
For the lips, I am currently using an 'Alba organics' vegan lip balm that I found in a health food store. I love it. It really feels good on the lips (not greasy or too thick), and I think it lasts a while. (That is, I don't feel the need to reapply it every few minutes.) It's also made with coconut oil, so it smells yummy. I have also tried Merry Hempsters vegan lip balm - I think it works well also, but it is a bit 'greasier' than the Alba organics stuff, although the Alba stuff is a little pricey.
Just FYI - I'm in my late 20s, and I'm at that weird stage where I still get acne but I also have dry, flaky skin. I have started looking at products intended for more 'mature' skin - they tend to moisturize better.
Hope this helps a little. Sorry I can't recommend the perfect products, but I think the products that work best vary from person to person.