No you can't fit injectors off a 2014 car into a 2006 car. The fuel injection system is completely different between the 2 cars.
Injection pressure on your car likely to be 1600 bar max, on a 2014 car 2000 bar.
It's unfortunate that there seems to be a manufacturing / quality issue with injectors on these cars resulting in much white smoke and poor fuel economy along with other issues.
To my knowledge Audi have never done a recall on these, I think some people have had a proportion of the cost of new injectors paid for by Audi as a matter of good will but they have been lower mileage cars with full service histories. And the work has to be done at a main dealer with the associated costs.
BMK info
http://www.volkspage.net/technik/ssp/ssp/SSP_350.pdf
CATA info
http://vwts.ru/engine/cata/pps_941803_3l_tdi_cata_w_clean_diesel_system_eng.pdf
Karl.