How do these two differ, for example:
寂しそう vs 寂しげ
楽しそう vs 楽しげ
言いたそう vs 言いたげ
大人げ vs 大人っぽい（...？ Not sure if this one works.)
They are the same ("seems like") but 〜げ has more of a connotation of 「それらしい」 or 「っぽい」with the げ coming from the character 気 as in 気分. I remember it as "that sort of feeling".
Arguably this makes 〜げ more subjective whereas 〜そう is more objective but only so far as the observation is shared with others in the same/similar view point as the speaker.
A word about usage:- You commonly use 〜げ when expressing your feelings. It comes from the kanji 気, so this serves as a reminder. It matters "what" you are talking about, not just that an adjective comes before it.
So observing the rule about expressing your feelings.
Alternatively these can be followed by に, as in 言いたげに見ている (looking with an expression of wanting to say something).
Origins:- Apparently this word has been around for sometime in certain parts of Japan (Ref: http://otasuke.goo-net.com/qa5447963.html?order=DESC&by=datetime > Answer 2), but some consider it to be 若者言葉 that is making the transition to accepted vocabulary (Ref: http://ja.wikipedia.org/wiki/%E8%8B%A5%E8%80%85%E8%A8%80%E8%91%890 + own experience)
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Well, basically ADJ-I's radical + げ means some sort of "with adj-as-a-noun"; it turns your adjective into a noun, expresses appearance. To make myself clear, let's see a few examples taken from the net:
Even though I've never encountered it, I infer that "言いたげ" means "with the apparent wish to say" (since the base was "言いたい", "I want to say"). In both cases, this is clearly something that you are observing. I think that you will mostly encounter げ+に or げ+な.
そう, on the other hand, is trickier. It's either your impression, or something you've heard.
For the last one, I'd say it doesn't work, since you're working with a noun. And appearance or hearsays with nouns is another topic…