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Check your case. Rag the tight places.
Give the tuba and case a sun bath for a couple of days
Lubricants may be the source of the fumes.

I've tried simple green, pledge, and dish soap with sponges to remove any lasting stuff on the horn but still smell it and can't play the horn too well. What can I use to get rid of it?

Have you tried wiping it down with Isopropyl Alcohol and good paper towels? If so and that still didn't clean it enough.......
MEK (Methyl Ethyl Keytone) available at Home Depot will remove any and all residue. Of course it will knock you out with the smell that's 10 times worse than Flitz and cause cancer but the nasty old Flitz smell will be gone. Do it outside with plenty of ventilation. Read all cautions on the can about wearing gloves and a respirator, etc.

WARNING: Do not even think about MEK on a lacquer horn and don't let it get in contact with the plastic finger button pearls.

I'm being funny about suggesting you use MEK. Having used Flitz though, it's hard to imaging it hangs around after being washed with Dawn Detergent and hot water. All I smell is Dawn Detergent after I wash Fltiz off a horn.

I think something else is going on and you really should air out the case and wash out the horn. Especially if you didn't wash off the horn right after using the Flitz. Good luck.

Get it ultrasounded then. When I got my tuba it was making me sick because it's almost impossible to not inhale at least some through the leadpipe. I got it ultrasounded. It was not at all filthy inside but there was some stuff in the leadpipe, he said, and the tuba has not made me sick since then. I do fine with my own spit and bugs, but not other peoples'

And thanks for the heads up on not using that stuff on my tuba. It can just get a little dull and I won't care.