Can an iPhone user read your iMessage messages?

Say they have an iphone, you have an iPod.
Do they have access to your messages?

If someone has the "read" stamp turned on in Settings > Messages > Turn on Read stamp, then you would be able to see it if they read your message. And if you have it turned, they would be able to see when you read their message.

You can set it up that way if both the ipod and iphone both share the same account as some people like having messages go both places, for example ipad, ipod and iphone can all get the imessage… But only if all are signed in with the same apple ID.

Yes, sure can!

Only if the both of you are using the same apple id. If not, then no they won't be able to read it.

No. The only way that they could see your messages is if they are signed into your Apple ID on their iPod in the messages setting. And they would only see the ones that were sent after they have signed in, the ones that were on there before hand they can't see.