I want to use the Linkedin API to get details of jobs posted by any company. This data seems to be public, so do I need to integrate Oauth?
The LinkedIn API isn't designed for developers to grab information and present it to people who haven't authenticated (public display). Making calls as a single authenticated user to store it or present it elsewhere is against the Terms of Use for the API. Additionally, you can't store the data you get - it's just designed to present to the authenticated user.
If you want to use the API to present this information, your users need to authenticate with LinkedIn and then you can make the call on their behalf. This is probably easiest to do using the Javascript framework.