If their counter to your opening seems awkward, finish development quickly so as to try and get a tempo advantage on them. You will be able to attack quicker and with a better standing/position. If they "attack too quickly", watch for blunders. Many lower rated opponents may make one.
Keep in mind this is all assuming your opponent plays badly in the opening. Their "strange" opening has a good chance of being sound if they play it right, or could have some gimmick to it that you don't know about.
I play against a lot of people who are self taught and don't follow the rules of sound openings. I routinely play against people who say as white I'm opening with the Ruy Lopez, when I play Bb7, they will play a6. How "bad" is that move on their part? Is there a way to exploit people who seem to attack too early in the opening?