The two other threads have been removed (received no answer). While cross-posting may seem like a handy way of trying to get a quicker answer, some users may not feel happy answering an issue in one thread, not realising that there may be already a good answer given in the other thread.
From what I would imagine, the noise is either coming from a poor cable/connection or the source VHS tape itself. If the sound on the tape does flutter or have background noise, this will be present in the re-recording. I would recommend playing back the original tape through the problematic scenes to see if this is the case. On the other hand, if the source tape sounds fine, check to make sure the cables are firmly pushed in or try a different cable. A continuous hum in the audio usually indicates that the cable has poor shielding and is picking the AC line sound. This can be checked by playing the VHS tape through your Lite-On to the TV, wiggling the connections and moving the cable about to see if this affects the audio. Finally, make sure the AV cable is not placed along any power cables.
The DVD media you use will have no impact on the audio or picture quality, unless it is poor to the point where the DVD player has problems playing it back, in which case both the picture and sound would start breaking up. Unfortunately, there is no way to correct the audio on a finalised DVD+R (or DVD-R) recording as these discs are "write-once", much like a print out on paper. I would suggest getting a hold of a DVD+RW or DVD-RW disc to try making test recordings when trying to rectify the problem as these discs can be erased or overwritten later like a VHS tape.