M.I.
I understand the irritation at finding yourself in a group of cliquey moms. I live in an area where most people have known each other for years, so it's harder to "break in" to the group. Have you tried to find groups based on an interest/skill/talent of yours? I know you probably want to find something kid-centered, but it may be easier to find something where you fit first, then you may be more likely to find someone you can be comfortable with and introduce the kids later. What about neighbors? Sometimes just the close proximity helps to create some type of bond. Is your child old enough to be in a pre-school setting, or get involved in youth activities like karate, soccer, etc? That may be a good way to meet people with similar interests. Not sure where you live, but try your local library or even Barnes & Noble, they almost always have a story hour that allows for the kids to have fun and the adults to chat a bit.
Another option is to start something yourself, but this may be a bit much. If you have a family-filled neighborhood, you could try to organize something for the moms and kids of all ages, or even just the moms. I know our neighborhood just started a "supper share", where once a month we all meet up and exchange meals with each other. It's a great way to meet and talk to other moms, and most of the kids are in the same age range (10 and under) so it helps to open up the mom/kid playtime opportunities.
Good luck! My husband grew up where we live now, so many of my friends are his family or friends, so I know how hard it can be to try and find your way in an area where it seems like they've known each other since diapers. Hopefully as your child gets a bit older, more opportunities to interact with others who share your interests will make it easier to find some people to connect with.