Tricky question, and not easily answered. I tend to learn vocab, when I can. If I practise the kanji strokes to the point of being able to write it without a hitch, great. But for the most part, it takes a lot of use and a lot of writing to remember the correct strokes. I have trouble with the finer details: remembering whether it's one radical or another, very similar radical, in any given part of the kanji. There are a lot of these instances (初 vs 社 - the left-hand radical; 矢 vs 失 - stick at the top or not, and both are used in a number of kanji). However, sometimes because you have to check so many times whether it is one or the other, you finally click and can recall a particular kanji perfectly. Sometimes it is the exceptions that make it stick.
As for readings, well, it really depends. I tend to stick with the rule that more often than not, if it doesn't have おくりがな, it uses the 音 reading. This isn't always the case, and sometimes you can't even remember whether one is 訓 or 音. I don't think it's that big a deal some of the time, so long as you practise seeing the kanji in different contexts and with different combinations -- something I don't do nearly often enough. I often rely on my keitai dictionary and can search using a "key word". So I just use a word I know to find a kanji, then check how it is pronounced when it is with other kanji. I seldom remember alternative readings or both 音 and 訓, but sometimes (after a lot of repeat looking up, usually), I will be able to guess the reading of a kanji combination -- or at least the parts I know.
I like plant and animal kanji. I find it fascinating to try and learn words that are not usually written using kanji. Take 薔薇 (バラ), for example. Very few Japanese people can write it (though all adults can read it). For some strange reason, I remember every single stroke as if they are etched in my mind. The same is true for a handful of insects and animals, such as 蜘蛛 (クモ), 麒麟 (キリン), and 鰤 (ブリ). I have no idea why I recall how to write them, but I guess it goes to show that when you are fascinated enough, your brain goes to the extra effort of affixing it in a more solid place of memory. If only it would work for the 常用漢字!
Actually, I've been trying to go through the school grade kanji. I work at a school and my interaction focuses mainly on the 4th grade. I have had a very hard time trying to learn 4th grade kanji with their combinations and 音 and 訓 readings. I don't even know most of the 3rd grade kanji yet! But every time I write either the kanji or the reading for a word, I am getting one step closer to actually knowing it. I guess you could say that without formal study, the study of kanji is very バラバラ*. ;)
(*Nothing to do with roses... just being poetic through phonemic association)