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A quick check reveals that the County of Cornwall was and still is the stronghold of this surname. The people of Cornwall had their own language when surnames were being adopted, so many Cornish surnames are from the Cornish language. A book I have on Cornish surnames explains Olds as being "from ALS; cliff, shore, strand."
I'm not convinced and would add the possibility that Olds is a version of Aldis, a female given name.