You can't reuse corks. You need a corker to insert them, and then use a cage to hold them in.
It's easy to get bungs/stoppers to fit them. I have several that I use for my "top off" wine when winemaking. A #6 stopper fits the gallon and 1/2 gallon growlers, and a smaller stopper (#3 or 4, check the size!) fits the bottles.
Broken Leg Brewery
Giving beer a leg to stand on since 2006