1. He tried to express his anger through his paintings.

2. He tried to express his anger with his paintings.

3. He tried to express his anger by his paintings.

4. He tried to express his anger _______ his paintings.
--------------------------------------
What prepositions can we use for the blanks? Which one is commonly used? Do we have some more prepositions which can be used in the blank?

The preposition "through" is best, but "with" also works. Instead of using "by" (which could mean "next to"), use "by means of." These also can work -- via, through the medium of, per.