They all seem to have a meaning related to 'shake' or 'shaking'.
The first one has readings 振る and　振るう
The next one has readings 震う　and 震える
The last one has too many readings and I don't know whats the point of that

Is it possible to create distinction between them?

I can't answer your question but... whenever I have used fureru with a japanese person they always interpreted it as 'to touch' (the other meaning). They have told me to use yureru instead. My impression is that fureru isnt often used in spoken Japanese.

If you can read japanese, check this thread out:
http://detail.chiebukuro.yahoo.co.jp/qa/...q149905579
They talk about the word ふるえる. Originally only 震える was used, but other kanjis have been used later on to add different nuances. Check out the first answer of that thread for more examples.

Anyway, don't stress it. Just learn to read them. You'll figure out the nuances etc. along the way.
But in my experience ふるえる is usually written 震える or 振える, 揺 is used when you talk about side to side shaking, f.ex 揺れる and 振 is almost always used for 振るう (ex:暴力を振るう).

すみません、リカイチャンの助けのおかげで　そんなに簡単な　日本語文書　が　よく　分かること　が　できますね。　ところで　私も　yahoo.co.jp　に　色々な　(愚かな　付き)　日本語文法や漢字の質問を問う　こと　が　あるのですか？　日本人と日本語が出来る方は 気にしません　ね？？

juniperpansy Wrote:I can't answer your question but... whenever I have used fureru with a japanese person they always interpreted it as 'to touch' (the other meaning).

Someone can correct me if I'm wrong, but I'm pretty sure ふるえる doesn't have a separate meaning of "to touch." Likely you mispronounced it and said ふれる(触れる) which does mean to [accidentally] touch.

There is also a 振れる（ふれる） 'to shake', but I'm not really clear on its usage. I've seen it once or twice in writing, but 震える （ふるえる）is far more common and useful (and the usual verb for 'trembling hand/lips/chest' in songs when someone is describing being overcome with emotion.)

揺れる is not 'trembling/shaking' but 'swaying/shaking', they're really quite different.
揺れる is also related to 揺る which is useful for when you grab someone by the shoulders and try to shake some sense into them, among other cases of shaking other things.

(Edit: Of course, 振る（ふる）which is useful for shaking a stick at someone is the same kanji as the ふれる that was mentioned as being confused with touching)