IR signals are sent as coded sequences, much like Morse code is. Here is one of the tutorials on IR codes: http://www.righto.com/2009/08/multi-protocol-infrared-remote-library.html
Now, whether or not the various IR libraries have been ported to the nano, I don't know. I know in some of them, due to trying to handle all of the different remote controls out in the world, take quite a bit of memory space, which might be problematical for the AVR's with limited memory. The library I linked to uses the PWM interrupt, which may be different on the nano (or you might want to use PWM on your own).
I haven't looked in detail at the libraries, but it is possible that the Arduino is locked up while it is waiting for the next command. That may be a problem for your blinking lights.
If you only had 2 buttons you were interested in, Sparkfun sells a programmable IR receiver that is a separate chip, and it raises one of two pins, depending on the button pressed. It has a learning function, so you can record two different key sequences. I just ordered it, so I don't have any experience with it. https://www.sparkfun.com/products/8753
Now, the company that makes the SIS-2 also makes a SIS-7C chip which supports 7 different buttons, which sounds like it might be more useful to you. Here is a link to their order page: http://www.simerec.com/order.html