what's law and rights in EU states? marriage with eu citizen

HI, every body.
i came in Lt as student,i can't continze my study so immigration cancel my card before 3month expiry date,but i don't nothing about it.i knew that day wen they cheak me one day that i am living illegal i said i don't know nothing becoz on my R card date was vailed 3 month more.
i am non-EU national,living in lithuania ,i am marriad in lithunia with lithuanian (eu citizen).i try to apply for family residence card but they didn't accept my docoments becoz saying i can't apply becoz i don't hve residency card and any vaild visa now:( as non-EU national i can't get residency card ?? i appeal in court but nothing result stil, can i travel in EU states with my wife ,with marriage certifecate and vaild passport?. imimgration saying u go out of schengen states and get visa from LT embassy then come and aply for family residency card , other wise we deport u by force becoz i am illegal, i don't hve right to get here visa ??as family member) some one can help me wat will be better that i will live with my wife be happily ligel ?
will be thanksfull