I think dish soap is way too harsh for their skin.  You might try using some kitten shampoo or baby shampoo.  I've also heard that if buck grease is especially thick, you can rub some olive oil onto it to thin it out and then either wash it off or let the rat lick it off.  But since he's so fat and can't reach it, you'll probably have to wash it off.  You could try feeding the skinny one extra-nutritious stuff separately.  Like take him out of the cage, and let him have some baby food, baby cereal, cooked mixed veggies, etc.

Deb

Dawn dish detergent helps -- but is very drying to the skin.  I second the vote on clipping the hair.  Your vet might even be able to do this. Then you can bathe him -- this body condition is a result of a very poor diet, poor guy! 

You can change his diet and feed him the normal amount of (nutritious) food -- but he may try to take food from his cage mate if he's used to a huge volume of food.  -- You'll have to separate them to feed them (or hand feed the big guy) or feed the normal sized rat extra nutrients on the side as Deb said.

He's lucky he has you.

Poor guy.  My boys have never had buck grease that bad, but it breaks up much more quickly if I rub them with olive oil first, then bathe them with Dawn dish liquid.  With how bad it is, you might want to let the oil set for several minutes after the rubdown.  After, I rub them with a bit more olive oil while they're still damp.

When Dana was alive, I just took her out for supplemental feedings a couple of times a day so as to keep the boys from getting extra food.  And to cut down on hoarding, I'd give each of them half a block at a time, so they'd each finish them around the same time.  If I'd put the daily amount in there, a certain someone would have just kept eating until they were gone. His brother wouldn't have gotten his share, and both might have felt hungry later in the day.  I had a plate of veggies (broccoli, brussels sprouts, other leafy greens) available all the time, and they each got about 2 to 2 1/2 blocks a day.  (For a rat as big as this guy, I'd probably start with three and cut down to 2 1/2 or 2 as he slims and you're able to see if he has a larger or smaller bone structure.)  They also get a snack of fruit/more sugary veggie every day, like a grape or small piece of apple or orange, or a carrot coin.

But then it was easy for me to feed them like that throughout the day, since I'm home all the time.  It made putting them on a diet easier, as I knew they never had to feel hungry.

Aw, poor little guy. I'd try the olive oil, and clipping the hair back.
Does he get any out of cage time? It's might help with losing weight.
A cage mate will also be helpful grooming wise.

Yeah, just switching to real food will probably show a huge improvement in his weight. 

When I had intact boys, I would rub a ton of olive oil into their skin on their back, and then wash them a couple times with dish soap.  Did the trick everytime!

And youch, he is so overweight    I would feed him a low-fat food such as Oxbow's Regal Rat with fresh veggies and fruit a few times a week to supplement.  Poor thing!

Four blocks a day is okay to start out with, but you should really restrict it more as he loses the weight.  It depends on what block you are feeding him and what the fat content is.  My boys get three medium sized blocks a day (Harlan 2014) and really that is more than they should be getting as they become less active with age.  One boy is getting fewer and the other more because of dominance problems so I'm having to work out a solution as well (though I don't think it will be as easy as yours!  ).

Is there a Walmart in your area?  They have a digital food scale that costs about $20.  That's what I use for my rats, and I love it because it also has a pan that sits on the scale.  It's great for putting the rat into so that it won't climb right off of the scale.

Deb

My boys gained nearly 100 grams apiece (so one was up to 700) over a three-week vacation, eating four blocks apiece.  As big as he is, he might lose on that amount at first, but it will probably need to be cut down to 3 pretty soon, then 2 1/2, then perhaps 2.

Maybe he's mostly spiky from the oil now, since it didn't all come off?  I have to watch how much oil I put on my boys after their bath.  If it's more than just a little bit on my palm, they look like I've styled their hair with gel.

Those pictures of him make me so sad.  It's wonderful he has someone to clean his poor little back and care about his diet now. 

When I had a rat with difficult buck grease I would comb the olive oil through his fur with a nit comb.  That really helped break up the grease and got it out really well.  You should be able to get one at your local drug store.  If I were you I would treat him for mites also.

Make sure and post after pictures for us.  I'm sure he'll be pretty once he's all cleaned up!

Ouch, it looks like it'd be painful for him to walk. I've never even seen that much buck grease before. Yikes! Good thing he has a nice, new, home now.

will he "walk about" ?? 

When I was trying to help Murphy lose weight, I had him walk the hallway several times a day.  I would shut all the doors so he could get into in of the rooms, then walk with him.  when he would stop walking, I would gentle nudge him with my foot.  I found it worked best if started as far away from the cage and had he walk toward the cage area, since he would hurry up heading back to his cage. 

good luck