Can you give us more complete specs of your computer please? "Asus motherboard" is like "chevy car". The actual motherboard make and model and revision if applicable and the cpu you're using may be helpful to this conversation. It probably isn't but you might as well list it anyways.
120/120 is more than fast enough for streaming video. About 12X more than fast enough actually. Please go to speedtest.net and hit "begin test" and see if you are truly getting 120/120 speeds.
If you are getting high speeds, then the only things that remain, as Bob said, you may need more RAM, less processes running, a better router, etc. If your desktop is on a wireless connection it would be very smart to hook it up with a wired connection as with most hardware, wireless will not be as fast as wired, and it will not be as reliable.
If you have a modern high speed router, having 4 people connected while you watch streams shouldn't be a big deal, unless they're all watching streams too or doing other data intensive work like multiple high bandwidth uploads/downloads, etc. For example, if you have 120mbps internet, and 4 people are on wifi, and 3 of them are downloading Steam games at 40mbps each, you're up a creek if you're the 4th person and you want to jump in and watch a high bitrate stream.
I'd suggest hooking yourself up to a wired connection, logging into the router, and turning the wifi speed down. Give each wifi user maybe 10mbps. It'll get them by and let you keep enough precious bandwidth to do whatever you want reliably and fast.
