How do you move an audio keyframe without changing volume level?

I'm assuming you're talking about doing this in the timeline on a clip, so if that's the case you can click on the keyframe so it's blue and then hold shiftto constrain your movement. If you hold Shift and then click the already blue keyframe then it will become deselected. You can also open the Effects Controls panel, click on the clip, twirl down the Volume parameters and twirl down Level. This will give you access to a linear view of the keyframes where you don't have to worry about accidentally changing the volume.