Is it legal for me to quit the agency which would mean having invalid J1 visa, go to US where my boyfriend lives and get married within a few days?

Generally, a foreign national who enters the U.S. lawfully and with inspection (such as entering with a J-1 visa), and who later becomes married to a U.S. citizen, may succeed in a marriage-based adjustment of status application process to become a Lawful Permanent Resident (to get a "Green Card"), and this is true even if the foreign national may have overstayed or otherwise violated the terms of her initial visa. The matter becomes significantly more complicated, however, if the foreign national were to be outside of the U.S. and were to be contemplating entering the U.S. with certain nonimmigrant (i.e. temporary) visas, including a J-1, in order to become married and remain in the U.S. permanently. The reason for this is that many nonimmigrant visas, including a J-1 visa, require "nonimmigrant intent," that is, an intention to remain temporarily and then return abroad after fulfilling the purpose of the initial visa. Promptly becoming married and then following-up with an application to adjust status may be viewed by immigration authorities as evidence of fraudulently having an immigrant intent when entering the U.S. with the nonimmigrant visa, and that can have very harsh immigration-related consequences. There really is no substitute for you and your fianc? to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.