I think everyone has their own "formula" for dealing with the side effects. Most people people on the interferons find that the side effects diminish over time. The one thing I'd point out to you about Tylenol is that it has the potential to damage the liver, as does Avonex. For that reason plus the fact that I am a drinker, I have always avoided Tylenol.
I use aspirin for the flu-like symptoms. Aspirin can cause internal bleeding. This has been exploited by the makers of non-aspirin pain reliever, but internal bleeding happens in less than 1 of every 500 people who use aspirin. For those who get an upset stomach, there is buffered or enteric coated aspirin. For sleeping problems, you can get aspirin with codeine. I believe this is available for the asking from the pharmacist, although I might be wrong and you could require a prescription.
Also, for sleeping problems there is a tea available from this shop
that does a great job. It is called "Good Night." Another idea is Valerian Root, which is available at any health food store.