This would generally be an issue with your capture device setup.
Unfortunately, your logfile indicates that the system you are using is VERY far below the minimum spec for OBS, and your test recording lost around 40% of the frames it was trying to record. Even if you get the audio issue sorted out, your recordings are going to be virtually unusable, with almost half of the video frames being skipped or dropped due to the system not being powerful enough to encode the incoming video in real-time.
A modern i5 if possible, an nVidia 900-series or newer GPU, 8GB RAM would be baselines. As far as the capture device, that depends on what your VCR can output... for strictly recording, older Elgato units will accept RCA or S-Video, and the inherent 2-second delay will not matter (since you're just recording, not livestreaming). There are a number like the HDCAP capture cards as well, and several based on the Yuan chipset that will capture analog video very nicely. Avoid anything by Hauppage like the plague.
If you're looking for maximum quality and price is less of a concern, a dedicated upscaler like the Framemeister mini-XRGB can be a worthwhile investment, and/or something along the lines of a Magewell Pro Capture capture card. This gets very pricey for the home user if you're just copying home movies, but in a corporate environment where you're trying to archive historical media for a business, can be well worth the thousand or so dollar investment to preserve as much quality from the source tapes as possible.