This app was mentioned in 2 comments, with an average of 1.50 upvotes
That's an MQTT server, and an app already exists for that
NodeMCU is a small development board with WiFi integrated into it, and it's compatible with the Arduino IDE. (It is actaully just an ESP8266 with breakout pins, voltage regulation, and USB). There are plenty of examples online, but the site for the library is here. I programmed in all of the IR codes for my devices (you hook up an IR receiver, had one laying around from another project - many tutorials on how to do this, and there are examples on github). I loaded the MQTT library onto the NodeMCU and had it listen for MQTT messages, and when it gets them, it fires off the IR LEDs hooked up with the codes I've defined.
You also need an MQTT broker (the server). I believe there are free ones online that you can use - I know Adafruit offers one. I haven't tried using them myself though. I have a Raspberry Pi hooked up to do this functionality, among other things.
On my Pi, I run OpenHAB to do all of the controls for my home automation setup. I have my Wink tied to it (rooted with the MQTT client on it sending updates and receiving commands), along with my Hue lights, receiver, sensors, and NodeMCU controlling my receiver (redundant, yes, but I realized my receiver had network capabilities later), projector, TV, and air conditioning through the IR LEDs.
OpenHAB is quite a bit to learn, and not exactly friendly when it comes to configuration at first. It is extremely powerful, and definitely overkill for just controlling a NodeMCU. You can use an Android MQTT client instead of OpenHAB as the client if you'd like. Probably much more user friendly.
If you have any questions, feel free to ask. I can shoot you my Arduino sketch if you'd like too. It would get you on the right track for sure. I'm not sure how much you know about programming or electronics, but I bet this would be a fun project either way and you're bound to learn something!
Edit: I say $3, because I had most of the things laying around my house. At minimum you'd need:
Optionally you'll need:
Bear in mind, getting the Raspberry Pi will allow you to play around in a Linux environment, and you'll be able to use it for other projects simultaneously! My Pi is: MQTT broker, torrent box, mini-NAS, OpenHAB server, web server, surveillance camera, and security system. I <3 my Pi.