Can I play videos from my Moto G on my Vizio TV via the USB port or HDMI. If possible, how?
There are a number of devices similar to ChromeCast which plug into the TV's HDMI port and accept wifi streaming from computers/phones/tablets. Some are quite inexpensive, and a few incorporate a full media computer running either Windows or Linux. Any of these will let you stream media to any HD TV, even a first year model.
If necessary, you could also use an HDMI switching cable to expand your port count, if all HDMI ports are already in use.