As a next step you could compare the version of Realtek drivers you have installed for those that are listed as compatible with your Realtek chipset on the Realtek website. The latest version listed is version 2.82.
If you look on the Realtek audio drivers download site ( https://realtek-down...om/download-hd/ ) you'll see a link to the Readme at the bottom of the list, and if you scroll down to page 10 you'll find the Realtek chipsets that are supported under that driver version says that it supports all chipset versions (in fact you need to go back to version 2.79 before you find that the supported chipsets are outlined individually as seen on page 31 & 32).
Back when I had a laptop with a Realtek chipset you needed to go through a complete Windows Control Panel uninstall/reboot/install new version cycle (which was a bit of a pain in the butt ... it was a Windows Vista operating system machine, so you can see I was working with early versions of the Realtek drivers). From what I read on page 2 of the readme in the Update Driver section it takes care of removing drivers automatically by running Setup.exe, rebooting when prompted and then it continues and finishes the new driver installation after restarting.
I would start by confirming that you are not already at the latest version (in other words I only suggest installing version 2.82 if you currently at an older driver version).
Two other avenues to explore (perhaps before doing the driver upgrade if you aren't currently at the latest version) is to check your Oblivion.ini for the current settings for bDSoundHWAcceleration (zero is disabled, 1 is enabled) and iMaxImpactSoundCount (will probably be set at 32, you could try setting it lower such as 24 or 16 to see if it helps).
The last possibility I can think of to suggest is an OBSE plugin named Trifle. One of the options it offers is the ability to turn off just the combat music (my theory here is that your problem is stemming from some problem related to just the game playing combat music, which in the default game starts often when an enemy is still some distance away but after they have detected you ... kind of fits with your reported symptoms).