The notes on this diagram apply to both variations of the puzzle.
The real puzzle has only eight colours but each quarter spoke is embossed with a circle or triangle and the casing is printed with coloured shapes to match. This is equivalent to having sixteen colours which was easier for me to model.

Reference diagram

diagram		 Definitions:
Regardless of the colours: spoke 1 is the leftmost forward facing spoke, 2 is the rightmost forward facing spoke and 3 and 4 are the rear spokes.
UR, UL,  DL  and DR are the four quarters of each spoke.

Moves:
1 = Spoke 1 clockwise 90o, 1' anticlockwise
U = upper casing clockwise, U' anticlockwise
Move sequence A
This sequence swaps UR1 with UL2 and UL1 with DL1.
Used for both levels of the puzzle.		 U 1 U' 1 U 1 1 U' 1 1
Move sequence B
This sequence swaps LL1 with LR1
It is not needed for the 8 colour puzzle.		 U' 2 U 2 U' 2 U    2' 1' U' 2' U 1 U 1' U'    1 1 A 1'
To describe this solution I sometimes indicate to invert the puzzle before sequence A. You can instead mentally adapt sequence A
Skip to 16 colour solution
Level 1 - 8 colours
Starting the puzzle
Complete spokes 4 and 3 by simple shunting. (because I solve quarters LL,LR,UR of a spoke first I often use sequence A to get the last quarter UL into position)
Then complete the bottom quarters and the upper right quarter of spoke 2 - this can also be done without any problem by simple shunting.
At this point the puzzle might be solved, but this is not likely...

If the UL2 is not correct
Rotate spoke 1 until the required colour is in UR1.
Apply move sequence A

Rotate 1 until UR1 contains the right colour.

Now solve spoke 1 if necessary

1. If UL1 and DL1 are swapped (but DR1 is OK)
Apply move sequence A
Solved

2. If DL1 and DR1 are swapped (but UL1 is OK)
Invert puzzle keeping spokes 1 and 3 in position
1' 2 A 2' 1
Solved

3. If DL1 needs to be in DR1 and UL1 needs to be in DL1
2 1 1 A 2' 1
Solved

4. If UL1 and DR1 are swapped (but DL1 is OK)
A
You now have case 3 above.

5. If DL1 needs to be in UL1 and DR1 needs to be in DL1
Invert puzzle keeping spokes 1 and 3 in position
1 A
Solved

Level 2 - 16 colours
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Starting the puzzle
Complete spokes 4 and 3 by simple shunting. Use sequence A along the way if it helps.
Then complete the bottom quarters and the upper right quarter of spoke 2 - this can also be done without any problem by simple shunting.
At this point the puzzle might be solved, but this is not likely...

If the UL2 is not correct
Rotate spoke 1 until the required colour is in UR1.
Apply move sequence A

Rotate 1 until UR1 contains the right colour.

Now solve spoke 1 if necessary

1. If DL1 and DR1 are swapped
Apply move sequence B
Solved

2. If UL1 and DL1 are swapped
1' B 1
Solved

3. If DL1 needs to be in DR1 and UL1 needs to be in DL1
1 B 1 1
Solved

4. If UL1 and DR1 are swapped
B
You now have case 5 below

 5. If DL1 needs to be in UL1 and DR1 needs to be in DL1
1 1  B  1'
Solved
1