If we cook pasta in a clean meat pot and pour it out (w/the boiling water) into a pasta strainer, does the strainer become “meaty”? Would I be able to later use the same strainer with pasta cooked in a dairy pot that would be put into a dairy recipe? (both pots were not used with their respective ‘genders’ meat and milk in 24 hours)

The strainer will not become fleishig or milchig in either case.

 

Sources:

1) The taste of the meat (or dairy) absorbed in the pot after 24 hours is טעם פגום ruined taste. (Shulchan Aruch Y.D. 122:1).

2) Additionally the taste of the meat is a נ”ט בר נ”ט דהיתירא (only a taste of a taste), see Shulchan Aruch Y.D. 95:1 & Aruch Hashulchan ibid:7).

This is not similar to the ruling of the the Shach 95:3 and Taz 95:4 (based on the Rema) that one should not cook a pareve food in a meat pot on condition to eat it with dairy — and some say not to do so even after 24 hours, if another pot is available — because we do not make נ”ט בר נ”ט initially. In the case of the strainer, it is not only after 24 hours, but the hot food is poured into a second pareve pot.