Wireless Power

For power, depending on what fixtures you have to power, one or more 12V batteries (car type, lithium-ion, ...) along with a 12VDC - 240 AC inverter will do. 

For dmx: wireless solution (wirelessdmx.com) or lumenradio are reliable options.

An easy option for the power would be a UPS like you would use to keep a computer running when the power goes out. It can be left plugged into the mains until the piece needs to move. Probably less to go wrong than making one yourself. 

I ve used the cheap donner wireless dmx sender receivers you can get on amazon and they seem to work fine. (Used them on my daughters wedding a couple of months back where I wanted to get dmx through a concrete floor at the reception venue - don’t ask!! )

ETC makes the ColorSource Relay with a wireless receiver. The relay will give you a remote on/off switch so you don't drain your batteries so much.

Check out RC4 products as well. Have used them with great success in the past. 

I use Li-po batteries because they are small and powerful. also wireless DMX units from ebay (budget constraints) and they work well.

I have also used car battery with an inverter for a small (400w) smoke machine on a portable prop.