Update: Fixed, kinda. The Oblivion.log file in the POL logs folder is about half the following two errors spammed hundreds of times:
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fixme:d3d:wined3d_check_device_format_conversion wined3d 0x153950, adapter_idx 0, device_type WINED3D_DEVICE_TYPE_REF, src_format WINED3DFMT_B5G6R5_UNORM, dst_format WINED3DFMT_B8G8R8X8_UNORM stub!
fixme:quartz:Parser_OutputPin_QueryInterface No interface for {56a868a5-0ad4-11ce-b03a-0020af0ba770}!
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I found similar threads on other games which suggested lowering the POL Display option for "Video memory size" to 3072. Amazingly that seems to have fixed it.
That of course limits my graphics ability. On a 14 year old game its not a huge deal, though I expect to see this again, and I like to max display options. It seems this isn't an uncommon problem.
Ubuntu 18.04 LTS
Video Card: GeForce GTX 1660 Ti, 6GB
POL 4.2.12
Wine 3.0