Strange Eggs are Eggs collected by Team GO Rocket. These Eggs generally hatch Poison-type Pokémon, Dark-type Pokémon, or Pokémon that acquire one of those types via Evolution. Defeat a Team GO Rocket Leader to receive a Strange Egg, and walk 12km to hatch it.
Note: You’ll need some space in your Egg inventory, Pokémon Storage, and Item Bag before your battle with Sierra, Cliff, or Arlo in order to receive a Strange Egg. You won’t be able to obtain Strange Eggs if you’re at or over your maximum Pokémon Storage, Egg inventory, or Item Bag capacity.