As they get older we are able to delegate more. Our oldest daughter is only 8 years old so she has only recently been able to start assisting with some minor cooking unsupervised. She is not able to cook a full meal though. At this point she is capable of making eggs and peeling/boiling vegetables. The children do help clean as well, but I find that the younger children (non school age) are generally more hindrance than help not because of ill will or laziness but because of incompetence/lack of physical strength. But as everyone gets older the children are progressively taking a greater share of chores. Our oldest son is 9 and he can help with yard work some but does not weigh enough to operate the riding lawn mower (plus is not tall enough to reach the pedals).
None of them are big enough to use the vacuum cleaner yet for example and brooms pose a challenge for them as well.
We had 5 children in 8 years though so when we first started homeschooling all of the children were still very young. It is getting better though. If the children were at a school there remains a lot of stuff that my wife could do that she doesn't have time for now (or lacks the fime to do it to the standard we would like -- maybe our standards are too high, I don't know).
There's an interesting Montessori list of "what children should be able to do at each age".
I have 1 ten year old boy, who is strong and heavy enough to run the riding lawn mower. But he only helps -- he can't do the whole 5 acres by himself. He's good at mowing, but not "finishing" (getting close to everything).
But my other 5 kids are girls, and all of them are skinny. The 7 year old easily handles a broom and dustpan. Between the 4 oldest, they do pretty much all the chores around here. I do outdoor stuff, and I use bleach and clean the toilets. I also have to supervise to make sure things get done. I do the dangerous things (e.g., dumping a pot of boiling water and potatoes into a colander). But that's about it.
Regarding vacuums -- perhaps yours is too heavy. We use a nice, lightweight one like this, which is almost a pleasure to use, even for the kids:http://amzn.to/29VC7CK
It actually vacuums, and it's easy to dump as well as de-hair with a sharp knife. But it does actually "suck" as opposed to the ones which just sweep.
For an even lighter vacuum:http://amzn.to/29VCVYf
Those only "sweep" but they do an amazing job considering how light they are, and considering even a girl can use it. Even if you had to use a "real" vacuum once a week, these would do a good enough job for daily use. Also, you can use them on hard floors as well as carpet. The kids especially enjoy using this kind of vacuum.