Which options in mechanical engineering lead to a career in oil and gas industry?

The courses which you have listed above are very basic level courses in mechanical engineering. Except energy and environment all other courses i.e.  Solid Mechanics, Machine Design and Manufacturing are taught in almost all of the mechanical engineering college and universities as compulsory/core courses. These are not usually offered as electives or optional subjects. Now that you have to choose two among these subjects , then you can choose any two of them. These are very basic level core courses and will not decide any future field of specialization. I shall suggest you Solid Mechanics and Manufacturing. These two courses and subjects are more close to career in oil and gas sector then rest of the two.