Firstly, wot roughbarked said above. Aim to build up your soils. I've got very similar soils to you and I feel your pain!
Gypsum, dolomite, and/or lime are all useful, both as claybreakers and to make your probably acid soils more alkaline. All the gardening mags say to dig it in but you probably find that this actually a useless exercise - it just sits there.
The best thing is to create raised garden beds. Even 30cm (one foot) above the ground, using sleepers or strawbales or anything will help. Buy in some decent compost soil (it's cheap if you do it in bulk - 1/4 square metre shouldn't cost more than $20, and that's enough to create a 1x2m bed) and combine it with no-dig garden principles to have something you can plant into immediately.
That'll sort out the shallow-rooted plants like your warrigal greens, midyimberries, strawberries, herbs, etc.
Now, go find Prostanthera spp - ovifolia or rotundifolia is best. These are the mintbushes and are extremely hardy, doing well in poor clay soils with low water and nasty frosts.
Dig the widest and deepest hole you can into your clay. Line it with some gypsum, straw and well-composted soil. Plant your mintbushes. Water for the first month or so and then ease off. They should flourish and presto! - you've got a nice minty herb.
Find some local species of acacia that will also cope with your conditions, and plant them. Ditto for eucalypts. I've got Eucalyptus olida - aka strawberry gum, aka forestberry herb - and it's doing quite nicely. Slowly, but not dying.
I also can't recommend highly enough having chooks. Chooks+bale of straw=soil, in just two weeks. Get yourself a chook tractor, and move it around the areas you want to improve. Plant in the mulch and compost they leave behind - plant _anything_, it doesn't matter what. Green manure if need be. Slash it down when it gets about 30cm tall, wait two weeks, add some plain soil, and then plant into that. (Note that this mix will be very high in nitrogen, and some natives won't deal well with that - you may need to reduce it down a bit).
Potatoes and Jerusalem artichokes, whilst not native, are excellent claybreakers - they even bring earthworms back into the soil (and oh yes, I speak from experience here!). I haven't tried the native equivalents of yam daisy but I do have vanilla lillies doing quite nicely in a raised bed.
Once you've got actual soil, then you can plant anything that will cope with your local climate :)