Q: Can I upgrade the processor and/or graphics card in my Macbook Pro?

No, the CPU is not upgradeable/replaceable.

The Intel Iris graphics is built into the CPU chip

If you buy a new one, you can.

https://www.apple.com/mac/compare/

The CPU and video chip are soldered to the main logic board of your MacBook, they therefore cannot be swapped out. Furthermore Apple do not have a scheme whereby you can trade-in your existing logic board and get a new one with (slightly) faster chips.

The effective option for upgrading to a faster CPU is to sell your existing laptop and buy a newer faster model.

With regards to the video chip, again as this is part of the logic board and cannot be swapped the answer is realistically the same. However theoretically with regards to the video chip you can buy a Thunderbolt to PCI expansion box, fit a standard PCIe video card in that expansion box and get a far more powerful video chip - even one in theory powerful enough to drive an Occulus Rift.

Unfortunately OS X cannot currently fully utilise a video card via an expansion box in this manner, Windows running on the same Mac via Boot Camp could. OS X can off-load some functions to a video card in this manner but I don't think this will help with running games.

See the following for some relevant information -

https://bizon-tech.com/us/bizonbox2-egpu.html/

http://www.xlr8yourmac.com/tips/MBP_ThunderBoltVideoCard.htm

http://www.journaldulapin.com/2013/08/24/a-thunderbolt-gpu-on-a-mac-how-to/