What is the attraction for them? If you can figure that out and remove it, they will give up.

Last year a friend had that problem and said using Terro ant killer finally resolved her problem. She applied it both inside and outside; drops of liquid on cardboard. She has no pets, but placed under tilted-up flower pots just in case...Good luck!

When I moved into my house a couple years ago, I had a terrible problem with ants in the kitchen. I did two things that seem (fingers crossed) to have fixed it.

One was to remove the ivy growing against the house. The ivy seemed to be a railroad for the ants. Second, I used the Terro ant baits - exactly according to the directions. For me that meant having a couple ant baits sitting on my kitchen counter for several days.

Here is a link that might be useful: Terro ant bait

Terro....... I've used it about a dozen times over the years and it works 100% of the time. Resist the urge to kill the hundreds of ants that will come to eat the terro.... they need to take it back to the nest. I put out a new batch every 18 hours or so until I don't see any ants for a full 24 hours.

There are dozens of different species of ants that invade US homes and they have different behaviors and appetites. If you can't ID the species of ant, you need to find out what they're eating. Then you can get a bait based on that food. Putting out sweet bait for ants interested in fat won't do any good.

Are they getting into food? And what types? That's what you need to bait. And don't just spray their paths--you need to remove their paths entirely.

Aaaaand, you're in Australia where all the critters are weird! :) You need local advice, like from a nearby university's entomology department or some sort of agricultural extension service.

I deal with MY ants by thoroughly cleaning their paths with window cleaner (because I don't mind the smell of it) and following the paths to where they enter the house. Then I'll caulk it or clean it or ignore it or rarely hit it with a persistent insecticide, JUST in that spot. But MY ants are mild mannered casual passers through. They're generally beneficial and don't really bother anyone.

(When I was in Texas and had fire ants, I was not so merciful.)

Thank you all for your suggestions. Terro is a none starter, 'cause, as fori noticed, and I forgot to tell you, I live in the Land of Oz.
Yes fori, a lot, but not all our critters are a bit on the weird side. A bit like some of the people :-).
I have done a bit of experimenting since the original post and have determined that they are chicken and tuna loving ants, but they don't like butter, avocardo or peanut butter.
I think the next option is to send some to the great formicarium in the sky by drowning them in vodka (mustn't be cruel - they have to go with smiles on their faces) then send them to the local Uni or the Government science body for an ID and more suggestions.
Again. Thanks for all your help.

Keep smiling.

Fof

Try sprinkling cinnamon in their path.

To get rid of ants you just have to wash away their scent trail. That is how they know where they are going. The last time I had ants I did that. They came in another way, I used a wet rag and washed away that trail. They were gone. That advice came out in our local newspaper.

I find where they are entering from outside. I often can eventually find a trail of ants crawling up the outside wall of my house and put ant bait there.

Then I clean up the ant trails inside the house by wiping the ants up with wet paper towels and quickly throwing the towels outside. They want food so provide it outside-tainted of course with poison. Also you want to kill them slowly so they bring the bait to the queen.

I had ant problems for years! Baby powder really helped- a hint from local tropical fish store. I kept sugar, cereal etc in fridge. I began cleaning with orange oil products which they hate. I found them carrying little termite larva off the roof! Once when we tented they were gone 3 years. I fried some bacon and they were back. Eventually I talked the neighbors into tenting for termites at the same time. The termite guy said my neighbors had a termite factory next door. Now I haven't seen them since! I don't fry bacon ever!

At one stage termites look a lot like ants. That is how we found them in my first home. I thought they were ants until I saw small transparent winds. I put a couple in a jar and call an exterminator.

Look for mud tunnels on the outside of your home, in the crawl space and in the garage. If you have paneling or sheet rock that looks like it's bubbled, that's termite damage.

@EmmaR
I don't know about termites in USA, but the Australian ones bare no similarity to ants. The winged or Alate caste of termites is equivalent to the flying ants and are both the males reproductive group. So fear not, mine are definately not termites, but some form of carniverous ant. Still awaiting feedback from the CSIRO.
I tried the cinnamon, Greywings, and that seemed to really piss them off, as they disappeared for a couple of days and then returned and started eating the castor sugar and borax barriers. Communal suicide????? :-))
Again, thanks to all you lovely peoples. I really love reading your suggestions.

Fof

We've had terrible problems the last year or two with little ants we have here in the US that are known as thief ants. They are ones that love fats, as well as corn products and it's amazing the things they will get into. My understanding is that our particular variety also comes from multi-queen colonies, so it's very tough to destroy the colony. I swore by terro before meeting these guys, who will not touch it.

Anywho, what I've had the most luck with is using a pyrethrin (sp?) based kitchen and pantry spray. Not sure if you would have such a product in Australia, but it's considered relatively safe (made from mums) and it's been the only thing that's affected the ants. I do have to make a point of respraying certain areas every few weeks and do larger areas at other times. I've always hated using more caustic products (and some people are rightfully wary of pyrethrins), but got to a point where nothing else deterred them, and was desperate. Fortunately the pyrethrins worked, or I'd probably had to go with something I REALLY didn't want to spray around the house.

These guys have permanently altered the way I live, even though it's been months since we've seen one. Fats are all stored in the fridge, lots of other things are in tightly sealed jars and bags. After we managed to effectively strangle them out of the kitchen, the darn things found their way to a hall cabinet where they took to devouring candles, lotions, and soaps, if you can believe it...

Sometimes diatomaceous earth, sprinkled liberally around the perimeter of the house, will deter ants. It needs to be reapplied after rain, though.