First, there is an amplifier in the Xonar. It is built onto the card.
Second, output is not measured by impedance, or Ohms. It is measured in Watts (W), or, in the case of a lot of headphone amps, milliwatts (mW).
AKG makes somewhat inefficient, difficult-to-drive headphones. You can find the efficiency of the headphones by looking at the listed sensitivity, measured in Decibels (dB).
There are more detailed ways to look at this, but you have to consider the output impedance of the amplifier with the impedance of the headphones. That tells you how efficiently power transfers from the amplifier to the headphones.
The impedance of the headphones tells you little about how hard they are to drive - you need more information. It's like trying to figure out how fast a car will go from 0-60MPH by only knowing the horsepower. Horsepower is part of it, but you also need to know the torque, gearing, vehicle weight, vehicle shape, road conditions, and a bunch of other factors.
Once you know how efficient the power transfers (it changes, depending on the impedance match), then you can figure out how much of the output power (mW) gets across to the headphones.
From there, you can use the amount of power that gets through to calculate how loud (dB) the headphones will get.
It's complicated and there's more to this, but that's a quick overview of what's happening.
As for your question, I'd only drive the K-702 with a quality desktop amplifier or an old receiver, if you want to save money. AKGs are tough to drive, so I wouldn't use a soundcard or portable amp.
