I'll take a bottom up approach.

a. Given enough normal stones, you can find the odd one in 2 stones by weighing one of them against a normal one.

b. If you know the 'direction' (wether the odd stone is lighter or heavier) you can find it in 3 stones by weighing two of them against each other

c. Given 5 stones and unknown direction you can end up with one of {a,b} by weighing 3 of them against 3 normal stones.

d. Given two groups (gl,gh) of 1 and 2 stones respectivly, and the information that if the odd stone is in gl it is lighter then a normal one, and if it is in gh is is heavier then a normal one:
weigh the two gl stones against each other, the odd stones is the lighter one, if they weigh the same the odd stone is the one from gh.

e. Given two groups (gl,gh) of 4 stones:
weigh 3 stones from gl and 2 from gh against 5 normal ones (6 would be easier).
- if the unknown stones are lighter we are left with the 3 from gl (case b)
- if they are heavier the 2 from gh (case b or a),
- otherwise the 2 remaining stones (case d)

f. Given 13 stones weigh 4 of them against 4 other. You either end up in case e or in case c with the 5 remaining stones.