Both have been selected under Australia's 'Giteau law', which provides exemption from the Rugby Australia policy of picking only home-based players.
Polota-Nau has reached the requisite minimum 60 caps for the Wallabies, while fellow Leicester team mate became eligible earlier this week after signing with local Super Rugby side Melbourne Rebels for next season.
Toomua was a surprise late inclusion in the Wallabies for their warmup match against a Super Rugby selection in Sydney on Friday.
Cheika also included six uncapped players in his squad, which he will trim next week ahead of the Rugby Championship opener against the All Blacks in Sydney on Aug. 18.
Melbourne prop Jermaine Ainsley and ACT Brumbies hooker Folau Faingaa are the only uncapped players in the forwards.
Outside back Tom Banks (Brumbies), Jack Maddocks (Rebels), Jordan Petaia (Queensland Reds) and centre Billy Meakes (Rebels) will also press for an international debut.
The All Blacks opener in Sydney also doubles as the first game of the annual Bledisloe Cup series contested between the nations.
The All Blacks have held the symbol of trans-Tasman supremacy since 2003.
Training squad:
Forwards - Jermaine Ainsley*, Allan Alaalatoa, Rory Arnold, Adam Coleman, Folau Faingaa*, Ned Hanigan, Michael Hooper (captain), Sekope Kepu, Tolu Latu, Brandon Paenga-Amosa, David Pocock, Tatafu Polota-Nau, Tom Robertson, Izack Rodda, Pete Samu, Rob Simmons, Scott Sio, Caleb Timu, Lukhan Tui, Taniela Tupou.
Backs - Tom Banks*, Kurtley Beale, Israel Folau, Bernard Foley, Will Genia, Dane Haylett-Petty, Reece Hodge, Marika Koroibete, Jack Maddocks*, Billy Meakes*, Sefa Naivalu, Jordan Petaia*, Nick Phipps, Joe Powell, Curtis Rona, Matt Toomua.
* denotes uncapped player
(Reporting by Greg Stutchbury; Editing by Ian Ransom)
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