I use Boraxo powdered hand soap and it really works. It's this grainy powder that scrubs your hands. It works every time. I don't mean to sound like an ad for the product, but this is what it says on the back of the can:
" Boraxo frees your hands from gardening gloves! Boraxo powdered hand soap removes dirt and soil from your hands. Its unique formula allows you to scrub your hands removing deep down dirt. Boraxo will remove most household and garden dirt."
It's no where near as harsh as dish washing liquid and my hands aren't as dried out, either. And it gets food smells off my hands, too.
The ingredients are sodium tetraborax decahydrate and 'fine toilet soap.'
Lanolin: try Lansinoh. It does not smell of anything. I first bought some when I was nursing my son, as it's meant for nursing mothers' sore nipples. I guess babies don't particularly like the taste or smell of sheep lanolin.

I don't use it on my hands, I use it as a lip balm now (haven't nursed in eight years.), in fact my whole family uses it as a lip balm. But my sister does use it on her hands.
Again, I really don't mean to sound like I'm advertising the Boroxo, but it's the one thing I found that actually gets dirt and motor oil and food smells off my hands.
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Edited to say, that Lee Valley scrub brush looks really good. I used one to prep my hands when I visited my premature niece in the NICU.
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