Any ideas on the best/easiest way to clean these up?

If you want a good job, the tyres, wheel nuts and caps need to be off the wheels.
Otherwise, remove wheel one at a time, remove centre cap; Septone "Al-brite" is an acid that will clean off the white aluminium oxide. Use a plastic dishwashing brush to apply and keep wet until it looks better; and rinse off. The diamond-cut outer steps from the tyre bead back to the knobs (spokes) can be cleaned up with wet/dry 320 grit paper (or finer grade) and then polished with Autosol.
With the tyre off, gutter scrapes can be filed out completely.

You could get them Hydroblasted, It'll bring them up like new.

My wheels were like yours and turned out like this.

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1970 MK II Cooper 'S' Supercharged 1310 with Megajolt.
1970 MK II Cooper 'S' Original resto project (SOLD)
1962 850 Original. (Under restoration)
1973 Leyland S (My first car. Now rebuilt, so my kids can learn how to drive a real car).
VMCI # 215.

Going off winabbey's gearbox components I would hydroblast them!

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1963 Morris 850 Smoke Grey
1963 Morris 850 Shadow Blue
1965 Morris Mini Smooth Van
1966 Morris Mini Van
1969 Morris Mini Deluxe Resto
5/72 Clubman Gt

+1 for hydroblasting.
But I hand sanded the spokes on mine. Then I put them in the big lathe at work, machined the gutter rash, then wet sanded with 400, 800 and 1200 paper.
After masking I painted the spokes with septone etch primer. And gloss black acrylic cans.
Finally polished with mother's mag wheel polish.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

Cheers, thank you