We don't use much. You can rephrase it "I have a lot of work which is not finished."

You might say, "I (still) have a lot of work left." (the "left," i.e. leftover, implies that your work is not yet finished).

Just add "so" then it should be fine for casual conversation. "I have SO much work which is not finished." Other way to say it is "I have so much unfinished work"

It is grammatically correct, but unnatural. To the native ear, it sounds very old-fashioned and awkward. A more normal and informal way of saying this is, for example: 'I've still got lots of work to do'.

I have a backlog of work that needs to be done.