OK lets try and get to the bottom of this rather than dancing around the subject.
First of all i dont think you have oodinium, its more likely to be Ich. If your fish had oodinium then its highly likely the entire tank would be dead within 1 week.
The symptoms of the Ich parasite and the oodinium parasite are very similar but the oodinium parasite id far more resistant to treatments and far more deadly (faster acting) than ich.
The only sure fire way of defeating either parasite is copper but as you have corals this simply cannot be added to the tank.
When anyone keeps tang i alway recomend preventative treatments as they are almost destined to catch ich at some point in their lifetime.
So although its easy to close the door after the horse has bolted (so to speak) I would recomend the following before a fish was added to your system (especially the tang).
UV filter
Ozone filter (better than a UV IMO)
Once the fish are in you should feed a diet that is treated with garlic.
And if the fish come down with the parasite then i recomend the following treatments that can be used in the tank.
Oodinex
Octozin
Ok so you are now limited on your options...
If you want to keep the fish inb the tank i would recomend that you start to feed with garlic and treat the tank with the above treatments. Add a UV sterilizer of an Ozone unit asap to help kill off any free swimming parasites.
If you were in a better position i would recomend this to deal with the parasite (I had to take this route when my tank was nearly wiped out with Oodinium).
Remove all fish and place them in a quarentine tank. Make sure you have some liverock or a very well mature filter that you are willing to sacrifice as it will not be able to be put back into the main system.
Dose the Quarentine tank with a copper based product, run a UV sterilizer in the Quarentine tank also if possible. Keep the fish in here until the main tank is ready.
The main tank needs an Ozone unit or UV system running on it. Raise the temperature of the tank (mine was running at 30-32 degrees from its usual 26 degrees)
Lower the salinity of the tank as low as you dare. I set my salinity to 1.018 which is as low as i dared to go. This did kill my sps corals such as acroporas but my clams softies and lps all surived this.
Then simply leave the tank alone and wait.
and wait
and wait
and wait some more.
I waited between 5 and 6 weeks before i was satisfied that the parasite was starved out and no longer a threat to my fish.
Once this was done i increased the salinity again, lowered the water temperature and finally added the fish back into the system. Before doing this however i did purchase 2 chromis and palced them in the quarentine tank so that the liverock (now imbedded with copper) would keep its bacteria colony well established if i ever had to introduce fish in an emergency once more.
My wifes Nano system recently got oodinium and suffered ghastly losses (the entire tank crashed within 24 hours). She wouldnt take my advice and re-introduced more fish within 1 week. They died within 24 hours
She finally relented and followed my advice and after 5 weeks she started re-stocking. She now has her nano looking batter than ever with very healthy and happy looking fish.
Sadly, Ich and Oodinium are very difficult parasites to fight in a reef system. They can be defeated but its gonna take time, patience and effort.
Lastly...
Im not sure on the size of your tank but it looks far too small for a tang wich really needs 100 gallons or more.
Considering tangs are highly stressed fish at the best of times its probably the initial reason why your tank came down with the parasite.
