Firstly how does one clean inside an aluminium Overton. A brass whistle . One problem. I’m severely nut allergic and Fairy liquid tastes vile.
You don’t need to oil metal whistles. Just swab them out well after playing if you’re a drooler or every couple of weeks if you’re not. As long as they’re clean and dry they’ll be fine. My Gens all have had their heads loosened, so I just pop the head off and push a wad of soft cloth through the bore. I also ran a wad of XXX-fine steel wool though the first time. I don’t know that it did much for the Gen, but it worked wonders on painted Feadogs by scouring out the paint that had been sprayed through the holes in the painting process.
The Overton you’ll have to clean by pushing a cloth in and then extracting it somehow. I use a .22 rifle cleaning rod for both, but you can use a small dowel for pushing and maybe twist something from stiff wire for the push-pull action.
I’ve been using a clarinet brush to swap out my whistles after use. Most music stores have several sizes depending on the weapon… err instrument. Inquire.. 
I use a wooden dowel of determined circumference and length, carefully cut out a small oblong hole close to one end ( It would resemble a flute cleaning rod but in wood) and then fold a shotgun cleaning pad through it and use that for a swab. A two inch square piece of old T-shirt would do also - or whatever size swab needed for the size of the bore. Low Ds need much larger than small bore high Ds.
BillG
What about the outside of a brass whistle. Once I actually used toothpaste because it made it really shine (no cavities, either!), but somebody recommended against that.
And what about the inside of the head…particularly the windway? That can get as gnarly as the tube.
Redwolf
Q-tips are good for cleaning inside the head if you can get it off. You might also be able to buy the longer ones used in doctors’ and vets’ offices.