How many modules can an Arduino Nano v3 support (in code)?
The devices will require some code to make them work and there is a chance, depending on how you write the code, that this may consume all the available RAM on the chip.  However I doubt you will go to more than 60% if you use the standard libraries for those devices, but there is only one way to find out...

Get the libraries for the devices and look at the examples for each device.  You should be able to hack an "example" of your own that calls all 4 examples in the main loop().  This should give you an idea of how much memory you are going to use.  

If you use too much it might be possible to snip pieces away from the libraries, the LCD will probably have font tables that you don't need for instance.  Or you could use an alternative Arduino.