You have conditions that are mutually exclusive - if meta_key is 'first_name', it can't also be 'yearofpassing'. Most likely you need your AND's to be OR's:
$result = mysql_query("SELECT user_id FROM wp_usermeta
WHERE (meta_key = 'first_name' AND meta_value = '$us_name')
OR (meta_key = 'yearofpassing' AND meta_value = '$us_yearselect')
OR (meta_key = 'u_city' AND meta_value = '$us_reg')
OR (meta_key = 'us_course' AND meta_value = '$us_course')")