How can I make non-Strange weapons count kills?

Strange weapons count kills. No other quality of weapon does. If you want a strange weapon, there are a few possibilities:

• If you want to acquire a new strange weapon, open crates, trade for them, or buy them on the market.
• If you want to make an existing weapon strange, you need a specific Strangifier. Note however two problems:
  • Only a select few weapons have Strangifiers available. The reason Strangifiers exist for these weapons is usually because they cannot be uncrated (and so can't be found as strange). The list is this:
    • Pretty Boy's Pocket Pistol
    • Cow Mangler 5000
    • Air Strike
    • Righteous Bison
    • Phlogistinator
    • Manmelter
    • Third Degree
    • Horseless Headless Horsemann's Headtaker
    • Widowmaker
    • Pomson 6000
    • Vaccinator
    • Classic
    • Cleaner's Carbine
    • Necro Smasher
  • Strangifiers are super-rare and consequently super-expensive. For example, last I checked on the market, the Strangifier for the Widowmaker was three times as expensive as an already-strange Widowmaker.
• If you're trying to get a strange decorated weapon (i.e. skins), you need a Civilian Grade Stat Clock item, which can make Civilian-grade (rank 1) weapons strange. Note that the clock itself can only be obtained by sacrificing 5 Freelance (rank 2) weapons or strange items, and can only be applied to Cilivian weapons; you can't add a clock to an existing weapon of higher grade.

Finally, note that some weapons just aren't available as strange at the moment.