The sound card will have no issue driving your headphones and use whichever setting works best for you. Start with the VoIP setting. If the headphones are not loud enough (when the inline volume is maxed), move to "Pro-Gaming" setting. I doubt that you will need to go to the "Exciter Mode".
The gain setting works like a headphone amp's volume control, except it is software based since the sound card puts out enough power to drive a all but the most difficult of loads. What it is actually doing via software is changing the voltage across the terminals. Had you been using the connection as a Line Out, say for a mixer, it might have been of consequence, to prevernt frying the Line In of that device. Further, it is a tool used to get the acceptable SNR when active devices are chained. Since the Sony 250 headphones are a passive device, you have to only worry that you dont drive those tiny speakers to their physical max. So, just turn the master volume down to 60% and then play with the gain setting.
All else being equal, high impedance cans need more voltage to get up to a similar listening level than low impedance cans. The Sony you listed are rated at 24 Ohms (no rated frequency) and sensitivity of 98dB/mW. For comparison, the iPod headphones are 23 Ohms (at 100Hz) and sensitivity of 109 dB/mW and Sennheiser HD650 is rated at 300 Ohms and 103 dB/mW. So clearly, the iPod headphones are the easiest to drive. The iPod buds and the Sony 250's will be much easier to drive to the same volume when compared to the Shenn. So looking at the size of the cans, you can guesstimate how easy or difficult they may be to drive, with a broad (but not always correct) generalization being, buds/in-ear (e.g. iPod style) are easier than on-ear (yours) are easier than around ear (Senn HD650).
