Straw results from threshing such as a grain crop. The litter may be chemically treated and may not decompose. The odor would be offensive. There is also concern about parasitic worms in meow dung. Best to mix with other products being composted and it would be better if sawdust was aged.
Worms help decompose organic matter in compost piles and in soils.
It isn't necessary to get rid of worms in completed compost. Heat will rid the pile while it is being composted.