The best hand cleaner after mechanical work is...

[zzyzzx]

I do what I can with this, or something very similar:

The stuff under my nails that I can not get easily will go away after a few days anyway.

 

[PandaBear]

Cheap lotion works surprisingly well for me

 

[Tempest]

Amsoil used to make (still does?) some hand cleaner that worked really well short of a break job. Cleaned well and didn't dry out your hands.

 

[Nick1994]

What breaks the oil and grit off good is the dry dishwasher soap, gritty enough to get the crud out.