I have been a huge Dallas Cowboys fan my entire life. I know exactly what you mean when you say you have weird things you do to help your team out. Here is some stuff I do -
1. Make sure I take a shower before a game starts. You don't want to feel all dirty or have your hair all messed up before a game starts. In my opinion it is bad luck and will make your team have a bad game.
2. Always have a drink right by you, and also some good snacks. Every time your team makes a good play, take a swig of your drink and eat some food. If they have a bad play, don't touch anything until their next good play. This works sometimes.
3. Always avoid all distractions around you. I will seriously ignore anything who talks to me while I am watching a game. If they walk in the room and say "hey, blah blah blah blah" I wont even respond.
4. Wear some of your teams apparel during the game. They can feel the extra support even if they live 1000+ miles away.
Try these out.