Why do transition metals have variable oxidation states?
Well, they have many orbitals of similar energy... so they can use them.
The possible oxidation states have already been shown here.
The d-block transition metals often use
...and the f-block transition metals often use
[This is the uranium complex known as tris(cyclopentadienyl)tert-butylisocyanouranium(III).]
Hence, the large pool of valence orbitals allow a flexible selection of oxidation states.