I suppose ´this/that kind of´ (adj.), ´this/that way´ (adv.) are all expressed with

                               böyle, şöyle, öyle.

Are they like any adjectives? How to choose between them?

Hmm.. I don´t think there is a strict distinction between öyle böyle and şöyle.  But I can give you some examples.

I think it´d be acceptable to say that öyle is used when describing something that happened in the past;

"öyle güzel bir düğündü ki, herkes aylar sonra bile onun hakkında konuşuyordu."

it was such a beautiful wedding that everyone was talking about it even after months."

and böyle when describing something in present, that you see or experience yourself;

"böyle güzel bir düğün çok pahalı tutmuş olmalı"

such a beautiful wedding must have cost a lot.

and

öyle can be used to describe things that you were not there to see for yourself, but were told by others.

"öyle güzel bir günmüş ki piknik yapmaya karar vermişler."

it was such a beautiful day that they decided to have a picnic(so was I told.)

Feel free to correct my theories about öyle and böyle=).

And as for şöyle, I really have no idea where it can be used.  I´ve heard it a couple of times but never bothered learning about it since öyle and böyle were good enough.

Yes, it helps. There seems to be a bigger distance to things that are described with öyle. The distance can be real or on the level of thought.

What is confusing about them is that they are derivations from bu, şu and o but they don´t seem to follow quite the same logics.

angel-of-death, thank you for replying.

You´re welcome!  It is a confusing topic, and to be honest after countless attempts to try and figure it out, I just gave up and started denying the existence of "şu" and its derivations in Turkish=).

I thought söyle is more like "speak, tell, or even sing"..  

şöyle, my friend, şöyle...

right.. Lol sorry.