Some people use rituals to cleanse people, places, or things that are believed to be cursed. What's important to remember is that it's not actually important what item or ritual is used, but that you believe that it works. Like I said before, it doesn't really matter what method you choose to get rid of a demon because it's all coming from the same basic premise - getting rid of negative energy and replacing it with positive (or at least neutral) energy.
The reason many Catholics choose exorcism rituals is simply because that's what they believe works. Other religions use other techniques because they believe that those techniques work for them. The key is knowing that positive energy is ALWAYS more powerful than negative energy. If you believe that all things are connected in the universe through our energy, as I do, then it becomes pretty easy to realize that you have an incredible amount of energy at your disposal. The energy that created all things is still in all things (even scientifically speaking everything and everyone in our universe is, at our cores, just collections of energy).
This source energy is called different things by different people - God, Source, Flow, Tao, etc. It's not really important to define it, only to believe that it exists. If there are rituals that make you feel powerful in a positive way, include those while you transform your energy and the energy surrounding you in a positive way. It's the belief that you are stronger than the demon (which is true) that gives you true power.