Not sure if I can help, not a dev and I'm not sure if I'm reading the log correctly, but I think the part that says "
Using auxilary audio input: Microphone (HD Webcam C270)" means your recording device is set to the audio of your webcam and not the audio of your mic. If so then make sure in the recording devices, (Taskbar>Right-Click Audio>Recording Devices and find your headset. Right-Click and set as default) then in OBS settings click Audio>Microphone/Auxiliary Audio Device and make sure it is set to your headset also. Oh and check Force Microphone/Auxiliary to Mono if it isn't. Another thing, if this works make sure (also in Audio) that you have Mic Sync Offset (milliseconds) set to the same as Advanced>Scene Buffering Time (milliseconds) so your mic audio isn't ahead of your video.
Hope that helped, if not then a dev will stop by I'm sure. Good luck!