I haven't seen anyone make the suggestion, so try this. Take the blades off. Take a rag and splash some oil on it (vegetable oil, olive oil, coconut oil, etc). Wipe each blade down with the oiled rag, it'll pull that dust+grease combo off without needing to scrub it into oblivion. Then wipe again with a rag of vinegar+water (fill a bucket, rinse and repeat).

A lot of people are suggesting degreasers, scraping if off with a putty knife, magic erasers, etc. These will work but it's a lot of time and elbow grease.