first: is your onboard audio limiting your headphones?
generally the v6 (the 7506 is basically revamped v6) is fairly easy to drive and unless you have very weak power output many devices should be able to drive them perfectly fine. if you note low volume output, tinny sounds, crackling, buzzing or any similar off-sounding audio then a cheap soundcard could certainly help (such as xonar dg) although if you are not having any issues i would say you are fine as amping them more than needed to power them is not going to generate a significant effect.
second: are your pc speakers limiting you?
i'm guessing you mean that you connect via a 3.5mm jack on the front of them. in short, if all connections are good no, it should have no effect on "quality" however, in some cases using the jack on the speakers can result in some emi/distortion from the speakers or crackling due to poor connections. also, the rear jack for speakers are not as heavily amped as the front headphone jack in some cases so they might sound a bit better or louder using the front jack.
at most i would say something like a xonar dg, but only if you feel it is worthwhile to do so because of issues. likewise for laptops a cheap fiio dac+amp or other device would work if you feel you have audio issues. you could spend more, but its completely optional.