I would add color with the new pieces. Or you could do all black and white.
The bed should be painted either black, white or the new color.

I have attached a photo of a children's bedroom in black and white with colorful walls as an example.

Why can't the ikea micke desk be spray painted to some colour that the other, lighter pieces would compliment. Personally, I don't think things should have to match; most things don't match they tend to compliment more often than match.

Another consideration: The ODDA wardrobe is black & white, the MICKE desk is black, go with that colour scheme for storage, shelving units, things that are vertical. The wood bed (horizontal) sets the 'rule' for things that are horizontal (flooring, 'floating' wall shelves, rugs, etc.) should be of the same natural material, texture, tone (wood). Curtains (vertical) compliment the black & white, bedspread, rugs, etc. (horizontal) compliment the wood bed.

It's not so much that there is wood and the black ikea desk but the styles of the furniture. If for instance you have a heavy, detailed wood bed it will never go with the desk no matter what you do. They will always look mismatched and odd.

I suggest you return/sell the desk or sell the bed or both. You can find a very well made used set in great condition in your local buy/sell ads normally under $300.00.

Thanks for the comments and suggestions, they have been really helpful. I think after discussing it with my son, we are going to go with the ODDA wardrobe, white kallax shelves, and a black bedside table, as the one he wants comes only in black, not white.
The wooden bed is simple, but functional for us as it is a twin bed, with another single under it, we use it quite often for visits and sleepovers and as it was an expensive bed I didn't want to get rid of it for the sake of its looks.
As for the desk, I would easily get rid, but my son really likes it and as it was his Xmas present last year from my in-laws, I had better just work with it!
The ODDA wardrobe is larger than the one he has so I think we can just not bother with the chest of drawers, and use the wardrobe instead. That in turn frees up some floor space so it won't feel too crowded.
Now I need to organise a trip to ikea :-)