No, the "western way of reading" isn't odd for the Japanese. This is for two main reasons:

1) Japanese can also be read left-to-right as western languages are and this style of writing is actually more common in modern Japan than vertical writing.

2) English part of compulsory education in Japan, so the majority of Japanese people are capable of reading English (which, of course, is read from left-to-right) to a certain degree.

However, for a westerner that has never been exposed to a writing system that features vertical writing, it can seem very strange to see this in Japan and in Japanese materials such as manga.