Strange weapons are obtained from unboxable crates.
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Weapons cannot be "leveled up" in TF2
No you cannot trade weapons for beta tf2 to normal tf2. Beta Tf2 is considered to be a completely different game by steam. Therefore the two game's inventories are not compatible.
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You can either play a lot and hope you get lucky. Or you can craft extra dropped weapons into hats.
Assuming this is TF2, you get it like any other weapon. Random drops on servers. It can also be found as a strange in the #30 crate.