Is double majoring in sociology and classics a good idea or will the work load be tough? And will I have a boost when it comes to job? Will the Latin and Greek in classics be hard? And will a double major be expensive for an international student? What are my job options?

At the end of the day, a key consideration about majors is whether there are job opportunities in that particular field. Once thing to consider is to perhaps choose a minor that will make your job search easier, like maybe getting a minor or take classes in the IT field, for example. This way you can still pursue your passion and at the same time give yourself more opportunities for job opportunities.

Yes the workload will be tough if you double major. I think when it comes to looking for a job after college it is more about what you learned in college and not really about what courses you took. If you can show a potential employer that you have experience in a particular subject (even if it is just educational experience) then they will count this as a qualification that you have. If you do decide to double major look for classes that count for both sociology and classics and that will help you decrease the workload.