Controlling 10+x 5m led strips with 10+ individual analog floor switches
I think that the best solution for you, unless you want a simple on/off control (if you want it just go with Majenko's solution) is to use port expanders.

Maybe this can be slightly overkill, but you can think of using a MAX7313.

This IC is I2C controlled and has 16 I/O; you can configure each as input or output, and with automatic PWM generation too. This means that the uC just has to send it the value of light you want to output and it automatically keeps the LED strips at the correct duty cycle.

This way you can connect a sensor to P0, P2, P4, ... and configure them as input, then a pull-up resistor and a MOSFET to P1, P3, P5, ... and configure them as output with PWM. From the arduino, you will just have to connect two pins (SDA, SCL) and, of course, GND, then you will have the ability to control eight sensor/led pairs to one sensor. You want to extend it? Just solder another IC and assign it another address (pins AD0..2 serve for this purpose). You can set 64 different addresses, thus being able to drive 512 sensor/led pairs.

Want more? Use RGB led strips. Connect P0 to sensor, P1 to R, P2 to G, P3 to B, and with each IC you'll be able to drive four sensor/led pairs. You'll be able to drive only 256 sensor/led pairs, but they will be rainbow colored...

This solution has only one drawback: I could not find any pre-made board with the MAX7313 on ebay. So you'll have to design your own PCB and solder it. If you are not able to do this, alternatives exist.

Adafruit has a PCA9685 16-channels port expander board (and a lot of other manufacturers made this). This has also integrated PWM and a lot of addresses possible, but the PCA has only outputs (so no inputs). You will be able to arrange them in a matrix (so with the 18 pins remainig you will be able to control 81 switches).

Another alternative is the MCP23017; this has inputs and outputs, but no automatic PWM; this means that if you want turn them on and iff ok, but if you want a variable light you will have to "manually" pull the pin high or low (very heavy on the I2C network).

Other solutions using SPI may have better performances (SPI is faster than I2C), and a lot of other ICs with SPI, I2C or other serial connections exist. You just have to find out the most suitable for you