Ink Plate – Eventhough printers have been using kerosene for decades, I prefer not to use it. Instead I use a little crisco vegetable shortening to remove the ink. You can use the oil, but I feel the shortening is alot less messy. I add a little crisco to a rag and rub it all over the ink plate. Once the crisco is rubbed all over, I take some clean paper towels and wipe off the crisco. Before inking the plate again make sure all the shortening is removed.
Rollers – I have used crisco on my rollers but soon found out that it did not completely remove the ink. For the rollers, I like to use California Wash made by Varn. The smell is not as strong as most solvents and you can dilute it with some water as well for economy.
Magnesium Plates – If you are completely against solvents, you can use crisco but I feel that a plate cleaner works best. I use ezi clean from RPB.
Hands – I love all purpose hand cleaner from E-Z Clean. Its blue and has a citrus scent. It does a great job removing all the ink from my hands and it doesnt dry them out either.
The company you buy your ink from will have comparable products to the ones listed above.