Sadly we don't even have an accessible loft let alone a garage. Although come to think of it there is some hidden space at the back of DD's cabin bed which is about the size of a couple of Ikea buckets - I had planned to rotate books using that space but maybe we could do one of books and one of toys. Unfortunately that space is currently so cluttered that I can't even get to it! So maybe that should be the first area I attack.
As it is, many of their toys are in our room (we have 2 of the tall Ikea Trofast units) although half the buckets are spread round the house along with their contents. Maybe if I sort that it all won't seem so bad. This thread has been really helpful in encouraging me to just do SOMETHING, however tiny, rather than worrying about the bigger project.
We don't have any relatives that we visit really but I could ask my mum if we could keep one box of toys and one box of books perhaps. I know she would like to see us more often and really loved having us to stay so I may be able to work with that. 
DD did ask me to put a decapitated broken doll in the bin earlier so perhaps there's hope at least for getting rid of broken stuff!
I won't do a massive "you must throw out loads of toys" drive, I agree that might upset them, but I will start keeping an eye out for small things that I can ask them about and I think DD will be encouraged if it means we can have playdates etc (much as I dread such things). My mum runs a small library and has asked for any unwanted toys for stay and play sessions so perhaps I could ask if DCs would like to 'help Nanny' and find things for her.
I have read some of Last Child in the Woods, it really made sense to me and DH. We limit iPad time but at present DVDs are limitless. It is hard to not rely on them when we are both exhausted and in pain but I think if the house is less cluttered - particularly their toys being more organised - it will be easier for them to play without the risk of being buried under an avalanche of random stuff.
Not read Simplicity Parenting but will look it up at work today!