I have heard it said that the reason as to why Ashkenazim place their mezuzot at an angle is to harmonise the opinion of Rashi, who held that it should be vertical (Menachot 33a, s.v. איסתוירא), with that of Rabbeinu Tam, who held that it should be horizontal (op.cit., s.v. הא דעבידא).
[See, for example, Sefer HaMaharil, §82 - here, lines 7-9]
If this is so, why do we not also harmonise between their opinions when it comes to the placement of the Sefer Torah in the aron, nor when it comes to the placement of the parchments in tefillin? In both of these cases, Rashi says that they are to be vertical and Rabbeinu Tam says that they are to be horizontal, and their reasons are the same as when it comes to mezuzot (cf: the Mordekhai, ibid., who quotes Rabbeinu Tam at length). In my experience, sifrei Torah are always vertically arranged, and I have never even heard of anybody with their tefillin parchments at an angle.