This is really tricky! Language is sometimes about a feeling. Of is a short, direct preposition and very natural to use.
With makes me think of having your hands full so it's quite intense.
Bored by = by indicates a cause, more factual.
From indicates a cause again, chairs are made from wood.
If you're talking about 'the same thing' or 'homework', I would use 'of' as it flows the best when speaking. If writing I would perhaps use 'with' to emphasise how boring and annoying it is.
Not clear-cut, but that's the beauty and flexibility of lanbguage and expression.
Hope it helps a bit!
Tutor Zowee :)