Is there a connection between Drain-Source voltage and Gate voltage?
The problem is that 3.3V and even 5V is not enough gate drive voltage to turn the IRF530 on to the desired degree to run a motor, it requires around 10V to be fully on. At 4V you can count on only 250 microamperes and to get the advertised Rds(on) of 0.16\$\Omega\$ (at 25°C, more when hot) you should give it 10V. 

Choose another MOSFET- a "logic level" type that has specified Rds(on) with your desired drive voltage (or less Vgs would be okay too). Refer to the datasheet: