Apply through the company website. Receive an invitation to network with existing exxonmobil employees. Subsequently, you will receive a call for the first interview, if you're shortlisted (1-2 weeks after networking session). If successful, you will be called up for second interview (2-3 weeks later).
Firist interview: Go through your resume. They will be very interested in your internship experiences. Followed by situational questions like resolving a conflict etc. Standard HR questions. Followed by a few technical questions to evaluate your though process
Second Interview: Easier than first imo. Go through your resume. Standard HR questions. More about what you can offer to the company so present yourself well and be passionate. No technical questions.