Not sure if there's some math behind it, or it gets updated based on backpack.tf price at some time, but you can take a look at https://scrap.tf/sitemap_1.txt or https://scrap.tf/sitemap_2.txt. There you can find a list of links to individual item prices sorted alphabetically, so prices of strange items are on sitemap_2. For example, if you want to know price of strange texas ten gallon you can see it at https://scrap.tf/item/strange-texas-ten-gallon
I can't guarantee that all of the strange items are in the list, but I guess it's better than nothing