The best thing to do would be to contact your orthodontist as they know what materials your retainers are made from and can give you the best information.
For my retainers (they are Hawley retainers), I have always used toothpaste and just brush my retainers whenever I brush my teeth. It is also a good idea to clean the case daily as well to prevent any growth of bacteria in the case.
If you have a clear container, then it may be necessary to use a specialty cleaner to avoid damaging the retainer. There are several types of available and your orthodontist can recommend what they think is best.
Efferdent is actually designed for cleaning dentures which are made of a very different material than retainers so it's best not to use that type of cleaner.