The third prong on the electrical cord is called an equipment ground. It's nice to have so you don't get a poke if you touch the fan while standing on a cement floor with bare feet. There is no threat of fire hazard for not having one though.
For instance, some guitar amps come with a ground lift switch in the event that you get a buzz through your guitar from lights being on the same circuit. You can throw the switch to cancel the equipment ground in the power cable and you won't be grounded with the lights anymore, but your amp won't blow up or catch on fire... unless you get carried away in the moment and do a Jimi Hendrix torch job on it.
The power strip is a good idea though. Most power strips have a surge protector or breaker switch in them that will kick off to protect your equipment in the event of an overload in the circuit due to a lightning strike or an electrical ground out such as your utility coming off the house from a tree limb falling on the wires, like what happened to me.
Just don't put more amperage draw on a circuit than the breaker is rated for. Try to spread out your lights, fans, air conditioners, dehumidifiers, humidifiers, etc... on separate circuits where all possible. Remember... safety first.