Will I be able to get No Criminal Record or Police Check from Australian embassy or consulate in China?

No.

Then, where can I get Australian No Criminal Record or Police Check?

Australian Federal Police in Australia.

Whether online application is available?

Yes.

Who can apply for Australian No Criminal Record or Police Check?

The Australian Federal Police (AFP) can only provide National Police Checks for:

1. residents of the Australian Capital Territory (ACT), Jervis Bay Territory and external Commonwealth territories
2. people seeking employment with the Commonwealth Government
3. people requiring a check under Commonwealth legislation
4. Australian immigration purposes
5. where the applicant resides overseas
6. overseas employment
7. overseas adoption
8. visa applications for overseas travel.

That's great, what do I need to prepare?

1. A valid credit/debit card for payment;
2. An email address for confirmation of submission and subsequent communication;
3. A PDF viewer; and
4. The ability to print and scan documents into .JPG .PDF or .TIF formats with each file being no more than 4 megabytes in size.

  Source: china.embassy.gov.au/bjng/Consular6_4.html & www.afp.gov.au/what-we-do/police-checks/national-police-checks