Which Parsha has the most Kriyos Hatorah from it?
The Parsha of Pinchas is the most often-read from sedra in the whole Torah (Rosh Chodesh & Yomim Toivim)
Just to add some spice to the answer I will add a story:
The Haflah, whose name was Pinchas, was Rav in Frankfurt. He was Chassidish and Frankfurt was not (to say the least). He had many people who did not appreciate him, and were open in their animosity towards him.
After he became Rav in Frankfurt he went to visit Poland where he was showered with many honors as it was more accepting of Chassidus. They asked him how is it in his own town they disrespected him and in Poland everyone bestows such honor upon him?
He answered: Simple! it is in the Torah. Parshas Pinchas always comes out in the Three weeks - a not so good time, but it is also lained on Yom Tov - a happy time.
I, Pinchas, am like Parshas Pinchas. In my own town, it is like Parshas Pinchas not such a positive time to lain, so I get not such a positive response. But when I am a guest it is like Yom Tov which is not the weeks Parsha but a guest Parsha, and everyone is happy with Pinchas then.