15 inputs, yes it can. The Uno has the 14 digital pins (12 if you want to use the serial monitor) and the 6 analog pins, that can also be digital in/outputs.
The best way to save pins would be to use shift register for the led strips and a multiplexer for the sensors.
As far as sensors, go you can have pressure, IR or ultrasonic sensors.
What is your spending budget? Different types of sensors cost more than others and you need 15.