You should take her to the vet if you are able to. Litter box avoidance can be a sign of a physical problem and 16 is fairly old for a cat.
oh oh..Oreo is trying to tell you something dear.......I will include a great article to read for you...
I will say tho, that cleaning a litter box weekly is simply not nearly enough, the best is to scoop it after every use...but if thats not possible than for SURE AT LEAST ONCE A DAY.....:)) keeps kitty happy:))
http://catinfo.org/?link=litterbox