Now and then you have to get serious about cleaning out your euphonium or tuba. It's not easy, because there are a lot of tubes and, in the case of compensating horns, a lot of corners and bends that are hard to get to. Here is my process. Note that I am describing the process for piston valve horns. You may want to adjust some of the steps if you have rotary valves.
The first step is to power-flush as much as you can out of the horn. You need a warm day for this. Take your horn outside where the garden hose is. Then dump a bunch of dishwashing soap down the bell. Wrap enough cloth around the end of the hose to make a seal about a foot down into the bell. When you have crammed the hose into the bell, turn the water on. The idea is to force the water through under pressure until it comes out the leadpipe (it should shoot out pretty well if you seal the bell-end correctly). As soon as the water comes out the other end, press down all the valves so the water/soap is forced through their tubes as well. This will stop the flow out of the leadpipe for a second. As soon as it flows out again, remove the hose. You want to leave as much soapy water in the horn as you can. If you let the water run too long the soap flushes out. Then lay the horn down and let the soap soak in a bit.
Then you want two plastic buckets or tubs, one filled with soapy water and one with clean water. After the horn has soaked for 15-30 minutes, put the hose back in the bell and rinse it out, remembering to press the valves to get the water through all the tubes. When you are convinced it is clear of soap, turn off the water and start to take the horn apart. Put all the metal parts into the bucket of soapy water. If there are any foam rubber bumpers inside the valves, put them in a cup to keep track of them. Also put any felt washers into the cup. For your valve pistons, unscrew the top button and remove it. There is probably a felt washer inside, which goes into the cup. Then take off the top cap. Under it there should be a felt washer, foam washer, cork bumper, or some other bumper. Remove it and place it in the cup. For horns that use a silicone bumper, that can go in the soapy water.
I have a couple of cleaning snakes that I use next. I take out each valve slide from the water and run the snake through it. After that I use the hose to force a stream of high pressure water through the tube. Then put the part in the pail of clean water. As much as possible, do this will all the parts. You should also run the end of the snake through each valve port. Be careful as you rinse those out because the water may follow a curve and come right back at you!
Once all this is done, I dump out the soapy water and rinse that bucket. The shake out each part and place it in the dry bucket. Then I take it all inside and prepare to reassemble the horn.
If the inner tuning slide tubes (that part that is hidden when you insert the slide into the horn) do not look smooth and shiny, you should use a little mild metal polish like Simichrome on them. Use slide grease (I prefer synthetic) and put all the slides in. Replace the bottom valve caps, but first put the slightest amount of grease on the threads so they don't freeze later. Insert the springs and oil and replace the valves. If the surface of the valves looks dirty or rough, try a little of the mild metal polish there as well. You should also make sure the top and bottom edges of the valve pistons are clean. Sometimes they can become grimy or corroded. Gently scrape off any residue that is there using a plastic scraper or even a wooden craft stick.
If your felt washers/bumpers have become compressed, try to find replacements. If you can not conveniently, then wash them as well. But do not squeeze them to dry them. Just set them on a paper towel for a day until they are dry. Otherwise you may cause them to compress and lose some of their softness.