Is it possible to move a wireless computer between two bikes? I have a cateye velo 7 wireless computer on a Hybrid bike and I use it mostly to check the speed and track my miles like an odometer. I love it, its simple and cheap and works.

I recently got a road bike that I am going to use on the weekends and but I want the same computer to track my miles. It is possible to have two sensors on two different bikes and use the same computer?

the wheel size on both 700C
It depends on the bike computer. 

Some computers have this feature, others don't. A brief look at the manual of this computer says yours only supports one bike and you'll need to get another computer for the other bike (or recalibrate it each time you swap them). 
If the tire sizes are the same, you might be able to get by by just swapping the computer between two sensors of the same type, but there may be enough sensor variation that the results may be off by a measurable amount, so I wouldn't recommend that. If the tire sizes are different, you'll obviously need to either recalibrate or have the computer have settings for 2 bikes since the circumferences are different. 

In any case, you need 2 sensors, and if you're using a cheap bike computer, the cost of the other sensor will be close to getting it with another of the same bike computer.