I want to play Minecraft with Iris Shaders (the Iris & Sodium version) whilst I have multiple other Forge mods installed. How do I do this?
You can't, at least not immediately.
Iris&Sodium is a Fabric based mod. As Fabric is currently incompatible with Forge and Forge mods, Iris&Sodium will not function 'out of box' with your other mod installations. As stated on the Wiki page linked above, it is theoretically possible to create a way to do so, but that would require knowledge about the innerworkings of both Fabric and Forge, as well as the time and effort to write, build, and test methods of combining the two.
I assume that there are projects out there to do this, but currently your best bet is to pick Forge or Fabric and stick to one of them.