A more detailed summary can be found here.

First of all, there are specific agents used to clean oxygen piping.  For example, “Blue Gold” .

Protocol for cleaning

1.  Inspect all elements of stainless steel piping
2. Flush pipes with deionized water (using a hand pump)
3. Clean through with aqueous, BlueGold solution
4. Flush until water flows clear for 5 minutes
5. Twice repeat steps 1 to 4
6. Dry the tubes by passing nitrogen through them
7. Flow nitrogen through until it is completely dry (hold a clean cloth at the end of the tube and check that no moisture is pushed through).
8. Once it’s dry, let the nitrogen flow for 15 minutes.
9. Repeat twice all steps, right from step 1
10. Reconnect, taking care not to accidentally introduce contaminants
11. Leak-check with helium
12. Pre-heat system for 6-8 hours and then sweep again with nitrogen

Quite a drastic amount of work.  All the best!