There are two primary methods for obtaining Strange Coins
1) While patrolling, the following can give Strange Coins:
- Bounty Bot bounties
- Patrol Chests
- Blue engrams (decrypting in the Tower)
- Any vender package will give 4
- The secret patrol mission will give you 2 (do 4-5 patrol beacons in a row without leaving the planet and it will show up)
The key is efficiency doing everything at the same time as fast as possible
2) Bring a fireteam and do Prison of Elders as fast as possible
- The final chests will drop them
- Blue engrams (decrypting in the Tower)
Additionally, Strange Coins can also drop as a Nightfall reward