Even though you switched from an IR major due to the economics requirement (which presumably has some math content), you needn’t write off your interest in IR entirely. While I agree that at least a basic knowledge of economics is important for IR, you might have other options to pursue your interest, even if you don’t major in IR. Many Russian programs offer a track in Russian Area Studies in which you can combine your language studies with coursework in Russian history, Russian politics, etc. In addition, some schools offer an interdisciplinary major in Russian/East European Studies. Either of these majors might be a viable alternative to an IR major, assuming that your that your main interest in IR was Russia. You also could do a major in political science since international relations is one of the subfields of that discipline. For a political science major, however, you probably will need to take a methodology course, which will include some math content in its statistics component. Another option would be to try to find an intro economics course with less of math focus, perhaps as a summer course or a community college course and try to transfer the credit to meet your school’s requirement for the IR major. You should keep in mind that if you should decide to do a professional master’s program in IR, you most likely will need basic coursework in economics either as part of the degree requirements or to be competitive for admission.
As for the recommendation of a minor in Professional and technical writing or some related to business, I think your advisor is trying to steer you toward something that will enhance your employment prospects. Language majors do best in the job market if they are able to combine their language skills with other skillsets. Also, for a Russian translation major, technical writing might be a reasonable option since you might find yourself translating technical documents. A business minor might not be feasible for you since it typically requires at least a basic economics course, so that might be a barrier for you. In general, for translation, it is usually recommended that you have an area of expertise to which you apply your translation skills.
As for a Japanese minor, I think it might not be the best option. For one thing, both Russian and Japanese are difficult languages and you might not be able to commit enough time to Japanese to develop enough proficiency to make it worth your while. Also, you should probably do a study abroad program in Russia and it’s unlikely it’s unlikely that you could study abroad in both Russia and Japan within a typical 4-year degree program. German or another Slavic language might be a better option. If you are a really strong language learner, other languages to consider would be Persian or Turkish, though their level of difficulty has some of the same drawbacks as Japanese.