Do I have any rights to get them moved?
If they service your house and no other houses, then you should be able to contact the various utility companies/agencies whose lines they are and request undergrounding of your service. Be aware that this will NOT be free of charge.
If they run across your yard and continue in both directions, odds are extremely high that they are in an easement and you have no right to get them relocated. You could try negotiating a new easement to replace the old one, but be aware that even if you are successful, you would be expected to pay all the costs of both the physical relocation and the legal relocation. I suspect the total bill would be eye-popping.
When you first bought your home, if your agent was on the ball, you included in your purchase contract a "title contingency" which specified that you were to receive a copy of the title report prior to purchase and could reject the purchase if there was anything bad in there. Hopefully you saved that title report, because the easement(s) giving the utility companies the right to run their lines across your property should be in there.
If you don't have a copy of your title report, you would have to either get a new report from one of the title companies or do your own digging in the county-maintained property records. I'd recommend first going to the website of the county recorder or other county official in charge of the public land records and seeing what you can find there. You can probably search on the property's tax ID number but some counties also allow searches by address or owner name. Some counties have scanned the old documents and put them online, but others only have newer documents online. Utility easements tend to date back at least as far as the creation date of the lot, so are often older documents.