If it is machine washable, toss it in the laundry! If not hand wash in a laundry tub or kitchen sink. Set in the sun to dry.
I would not put it in the washing machine if it contains any grease, oil, or fuel. You risk it getting under the rubber edges and into the hoses. Also, due to its shape and stiff seams, the bag is not going to collapse and turn over well during agitation. It will most likely balloon up with water and air and throw your tub off balance in the spin cycle.
I would instead take it outside on a solid surface such as patio concrete. Give it a big dousing of pre-treat laundry spray such as Resolve, Shout, etc. Scrub with a non abrasive hand brush, rinsing with water from the garden hose. Then wash with a mixture of diluted dishwashing liquid detergent and hot water, and drip dry.
If you have access to a spray power washer use that. We clean our car carpet with one and they come out like new. A little Dawn would help and rinse till the water runs clear.
Have him do it!!!!
Yeah he should!
All of the previous answers are great ways to clean things, but this should have been cleaned numerous times before it got in this condition. If it were me, I'd toss it and get a new one.
Your husband's bag shows lots of hard work and that is awesome!
I use dawn prewash on oily things and does wonders. I would treat it and let set and then spray it off outside. Then I would try an upholstery cleaner and / or read up on goof-off or one of the degreaser hand soaps(Goop, Permatex, Go Jo, etc.) and try that in one of the remaining soiled area before doing to entire bag in case of discoloring.
If it comes reasonably clean, you might want to spray with fabric protectant (Baye's says protects against oil) to see if it will slow down future stains.
Shout makes an aerosol cleaner specifically for grease. My husband comes daily with greasy shirts and this is the only thing that will clean them even after I’ve missed a spot, noticed it when it comes out of the dryer and it can still be saved with this miracle in a can by Shout. The trick is to make sure The bag is slightly damp spray with the Shout grease remover and let sit overnight then machine wash. It works every time!