Ahnika Grantham contains the methods for reciting Astakshara, Dvaya mantras, etc. There are differences in traditions that require Astakshara mantra to be chanted either standing or seated.
As far as Dvaya mantram and Carama slokam, they must chant while seated. I think they cannot be recited while standing.
Tiruvastakshara mantram is to be recited based on the respective traditions followed.
It is a practice for ladies to recite Astakshara mantram and Dvayam mantram while sitting. After reciting the Dhyana sloka taught by the Acarya first, the japam must be done with the eyes closed, hand covered with a cloth for keeping count, as taught by the Acarya. Astakshara mantram, Davaya mantram and Carama slokam must be recited a minimum of 10 counts.