Screw strands; they have nothing to do with wafers. At all. Adamantine actually extracts to strands, then there is a specific "custom" reaction (as in, it has the listing and setup in reaction_standard) to turn adamantine strands into, not adamantine wafers, but adamantine bars. In fact, the [WAFERS] tag, added to a metal in the metal's matgloss, is what makes adamantine make wafers, and adamantine bars are literally impossible (because it has wafers instead). So, if you make tungsten strands, you'll then need a custom reaction to turn the strands into bars (which will appear as wafers if you give the tungsten metal the [WAFERS] tag and will count as 1 mat_size for creating things instead of 3, like bars do).
So, you could put the [WAFERS] tag on tungsten and manganese, then make Wolframite that would have the [ORE_METAL:TUNGSTEN:100], [ORE_METAL:IRON:50], and [ORE_METAL:MANGANESE:50] tags. When smelted via the "smelt wolframite ore" option, which you wouldn't have to make a reaction for as ore reactions are coded via the [ORE_METAL tag, you'd have a 100% chance of getting a tungsten wafer (not a tungsten bar!), a 50% chance of getting an iron bar, and a 50% chance of getting a manganese wafer (again, not a manganese bar).
I don't believe that there is any way to extract strands from an item and also get a bar out of it, and I am uncertain as to whether or not you can extract more than one type of strand from one bit of ore, so it's probably best just to skip it.