Don't move it to the garage!
Think of each item of clutter as a decision that has been deferred. If you move it out of sight, it's easier to keep deferring. Instead, you need to make the decisions. Making the decisions of where things should 'live' can take a while to work out what works for you, but once it's done you shouldn't have to think about it any more.
WHAT are you bits and bobs that have no home? Do any of them fall into categories that sort of belong together? That means you can give them a natural home together.
Also remember: try to make it somewhere EASY to put away into. If it as little effort to put away properly as it is to dump in a corner, then you are far more likely to put it away properly.
For example, I have a box for storing what I think of as "stuff used for sticking things to other things". So: sticky tape, duct tape, electricians tape, glue, blue-tac, glue sticks, and so on. This is the only place in the house where they are kept. So looking for 'sticky stuff' doesn't require any mental effort, and putting it back there doesn't require any mental effort either.
Next to that box I have a box with batteries. Every single battery in the house is in that box. Next to it is a bag for old batteries, so that whenever a battery is changed, the old one goes straight in there. Then they get taken for battery recycling when it gets too full.
It won't take forever. But it probably won't happen overnight either. 