Google doesn't say anything about Nexus device sales, but Asustek, the manufacturer of the Nexus 7, does. The chart below, from the Q3 IR deck, shows tablet unit sales for the first three quarters of 2012: today it announced that total tablet sales in 2012 were 6.3m units (in line with a target it stated in December). 

The Nexus 7 went on sale in Q3, and in October the CEO was quoted as saying: "at the beginning, it was, for instance, 500K units a month, then maybe 600, 700K. This latest month, it was close to 1 million." (link)

So:

• Around 4.8m tablets sold by the company since the Nexus 7 went on sale
• Verbal comments indicate 2.1-2.2m in Q3, which is consistent with the total figure
• However, that would imply a collapse in sales of all other products (616k in Q2), and might perhaps include product ramp-up in June
• 2.4m tablets sold in Q4
• Therefore total possible Nexus 7 sales of say 2.2m in Q2/Q3, plus at most 2.4m in Q4, and probably a hundred thousand or so less (given sales of other devices)
• Hence, total Nexus 7 sales of 4.5m to 4.6m, and no more than 4.8m

It's worth pointing out that Nexus 7 distribution was somewhat patchy - for example, it only went on sale in Japan at the end of September. 

Apple doesn't disclose iPad Mini sales separately, but going on the ASP, my estimate is that it sold 10m in Q4, despite the fact that it wasn't available until the beginning of November. 

Kindle Fire sales numbers aren't much better than guesswork, given that Amazon doesn't disclose anything, but my guess is that it outsold the Nexus 7 as well.

I'll update this if and when Asus gives more precise unit sales (the investor conference is on 5 March).