Soil improvement - soil smells foul

It sounds like you have what is called 'Gleying' where water doesn't drain away causing the iron in the soil to reduce to the ferrous form.
You often get a sulphurous smell.
Dig in plenty of compost and sharp sand (not builders) to aid drainage.

Horticultural grit is an alternative to sharp sand

If you are growing vegetables I would dig out paths and put the extra soil in raised beds, lay bark on the paths and you won't be squelching between beds. Raising the beds will help the drainage problem.
If you start a compost bin or two with all your kitchen waste weeds etc
use it to mulch the soil in late winter and the worms will dig it in.
My son got me a nice tiller machine from Liddles, It was just under £40, that might save some back breaking work and help break down the clay. Once you have the soil in good condition, keep mulching with compost and it will retain nutrients better than a sandy soil.

Best of luck with this; I have been battling against heavy clay with poor drainage for years. Every year we dig in grit, sand, soil conditioner, compost, bark, we've tried the lot & every year I feel like i am starting afresh, its hard work but dont let it defeat you. Grasses do well (large ones help soak up some of the moisture), astilbes, ferns are good. Campanula, foxgloves, sidalcia, poppies, hebes, fuschia, paeony, roses, polemonium, aquilegia, veronicas, ribes among others all do well in my garden so with a bit of trial & error you will find what works for you. In the summer, hoe very regularly to losen the surface or it sets like concrete. When the digging gets a bit much just remember all those nutrients that are in clay soil.

I give my clay soil a good dose of manure, compost and any other bargain soil improver I can get hold of each winter. The soil's getting better year on year. I spread a couple of inches over the surface and churn it well in with a four pronged cultivator. It might sound crude but I'm well pleased with the results.

I had heavy clay soil when I first started working my garden and was told to add gypsum & dolamite and till it in. Then add the compost, grasses, chicken poo & sand. The flat clay plates are opened up with the gypsum & dolamite. It worked very well~