I am in the process of selling my property in australia, and am now living in the US, having recently got married to a US citizen. Once the property is sold, if I transfer smallish amounts over to my US bank account via wire transfer, am I subject to US tax. Also does any of this affect my husbands tax position?
Thanks for any comments.

There are no transfer taxes in the United States. If the amount transferred exceeds $100,00, you may have to file Form 3520 to explain from WHERE the money came, but, other than that, you are okay.

Now, the sale itself may be subject to capital gains taxes. It depends on whether the house was your primary residence or not.

If you are resident of U.S. you must report worldwide income (including sale of foreign property) on your tax return.
You must also be aware of forms TD F 90-22.1 (also known as FBAR) and 8938 Specified foreign financial assets (SFFA). Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income (http://taxipay.blogspot.com/2008/03/us-citizen-or-resident-with-foreign.html)

At present my status is I believe resident-alien. My application for "Adjustment of Status" after marriage, has been submitted and Im waiting for my green card. I would not have thought I would have to fill out a tax return; I am not working either. My thoughts are that the income from the sale of my house is purely a matter for Australian Tax Authorities if any, and that the US authorities shouldn't have any jurisdiction over proceeds earned from the sale of an Australian property, even if I choose to transfer some of it over to the US. Wouldn't this be the case?

Not if you file jointly with your wife and CHOOSE to be treated as a resident alien. When that happens, ALL world-wide income is subject to U.S. income taxes, to include the procveeds from the sale of your house.

Now, if you are still categorized as a dual-status alien for 2012 and you do NOT file jointly with your American spouse, then MAYBE the proceeds from the sale of the Australian house is NOT considered for your 2012 taxes. It depends when the sale is finalized (beofre or after the green card is granted).