We have used dish washing liquid in the waste tanks to help clean them. Not packets but gel/liquid that is diluted and poured in. It seems to have good de-greasing and "wetting" agents and for us helped get the gunk out and make the level sensors work better. Preventative maintenance is your best action though. Don't scrape dishes into the drain. Scrape and wipe the dishes, pots, skillets, into the garbage so that what goes down the drain has as little food and grease as possible.
As far as a blocked grey tank, unless the tanks have been severely abused by not taking the preventative maintenance, other than construction debris it's hard to imagine normal grey tank "stuff" clogging it up.
2020 Keystone Raptor 356
2012 PT Crusader 355BHQ (GFs)
2020 Ram Laramie 3500 DRW CC 4WD Diesel