There have been 50 occasions to date when every member of a Test eleven had scored a first-class hundred before the beginning of the match. It has happened 23 times with England, ten each with Australia and India, three times with New Zealand, twice with South Africa, and once each for Pakistan and Zimbabwe. Results have been 16 wins, 13 defeats and 21 draws. Australia did not win any of her matches with eleven centurions.
The first occurrence was for England against Australia at The Oval in 1886, and the most recent for India against Australia at Dharamshala in March 2017.
Concentrating just on these matches, one way of measuring the strength of the lower order would be to look at the four “worst” batsmen in each team. This could be done by taking the lowest four final first-class career averages, and calculating the combined average of the four. For simplicity all averages are rounded down to the nearest whole number. The batsmen identified can have batted anywhere in the order on the day, not necessarily from 8 to 11.
Several of the teams have been mentioned on this thread already:
The “worst” four batsmen of the 1902 England team have a combined first-class career average of 25. In ascending order they were Lockwood, Braund, Lilley and Rhodes. The equivalent figure for England's first such team in 1886 was 19.
The South African combination of 1907 scores 21. All eleven averaged at least twenty in first-class cricket, but only Nourse and Faulkner over thirty.
Australia's best score is 27 against Pakistan in 1959, represented by Lindwall, Grout, Davidson and Benaud. In 1956 alone the Aussies fielded no fewer than five Test elevens with eleven first-class centurions.
The South Africans at Adelaide in December 1998 return a high figure of 30, thanks to Richardson, Symcox, Pollock and Bacher. This is matched by New Zealand a few months later at Old Trafford.
England's eleven against Bangladesh in 2016 was actually “strengthened” a few weeks later in Rajkot when Ansari replaced Batty, to give a reading of 28.
The highest such score ever recorded is 34 by India against West Indies in Delhi, November 1983, courtesy of the World Cup winners mentioned earlier in the thread. This is the only instance of all eleven men not only having scored centuries, but also finishing with a first-class average over thirty.
The next highest (31) was also for India against West Indies, in 1962. This time only keeper Kunderam averaged under thirty. It did not prevent India losing the series 5-0.
Pakistan's eleven centurions appeared against India at Lahore in 1989, and Zimbabwe's at Perth in 2003.
Only once have all twenty-two players in a Test match scored a first-class hundred beforehand: England v Australia at Lord's in 1905.