No employer is going to let you have 3 months off but maybe sacrificing a couple of days in the new year to have a long weekend to do it might not be a bad idea.
Now, you need to have a clear route for everything that you sort as in bin, donate or keep.
Anything you do keep must be kept somewhere practical as yes, it's lovely to keep 500 photos but not if you end up storing them on the dining room table for 3 months whilst more clutter accumulates around the pile.
When you say stuff could be useful to people do you mean for those in your house like hand me down clothes amongst the kids or are you talking about the screwdriver set you've had for years and never actually used??
A lot of useful stuff can be donated so just get rid of it. Find your local charity shop and incorporate in to your school run or on the way to work or even taking the kids swimming. There's charity shop next to the sports centre where we go swimming, so I take a bag full of donations with me when I need to.
Even joining your local Facebook community page to give stuff can clear a bit.
Throw things away, bag it up, and in the bin it goes, especially the day before bin collection day, if you have space still in the bin, grab a bag, fill it and out the house it goes.
Don't feel guilty about throwing stuff out or donating it, because look at the grief its now causing you. All this stuff is really weighing you down mentally, is it really worth it?
You can do this but it will take time, Rome wasn't built in a day and all that.