How to power my Arduino mini using wall socket?
I have connected the Relay and IR receiver directly to the Arduino
  mini. Pin 10-14 are used for the relays Ins and PWD 3 for IR output.


I hope you don't mean that you have connected the coils of the relays directly to the Arduino pins. If that's the case, the surprise won't be the regulator blowing up, but the MCU surviving. Please edit the post and add complete schematics and/or photos of your prototype.


  The mini works with these 5V mobile chargers but the amount it heats
  up scares me. Any suggestions on what I should do.?


Use a small heatsink if you're concerned about the regulator heating up. But it really shouldn't be a problem unless you're driving too much current from it. Have you actually measured the temperature it reaches?

Also, don't feed the coil through the regulator, but directly from the 5V adapter (presuming your relays are 5V). This will save a lot of dissipation in the regulator. NOTE: don't do this if you use a higher (> 5) voltage adapter!!


  Also how much current consumption would be needed. I have tried using
  a 5V 300mA charger and 5V 700mA charger. Both work almost the same.
  Why?


Those current ratings are maximum values, not constant values. So, if your circuit draws let's say 290 mA, both adapters will be able to do the job.

EDIT: additional information 

To safely and properly use relays with arduino, you need some interfacing electronics like this:



Full article from the source, here. Flyback diode: 1N4148. You can use almost any "logic-level" N-channel MOSFET.

If you're using instead a relay module similar to the shown below, all the required interfacing electronics are already built into it and your digital pins won't suffer any overcurrent condition.



However, the regulator will (probably) still suffer from excessive current through it. In some of these relay modules you can optionally use a different power line (JD-VCC, see below) for the relay coil. If you own one of these, feed it directly from the 5V adapter, skipping the regulator.



If the relay module doesn't have a separate power line, it may still work when connected to the 5V adapter if the dropout in the regulator is not too big (i.e., the "high" level from the digital pins is not too far away from the adapter voltage).