Moved blog to self-host, now old posts are 'reposting'

Is it WP…?

Unlikely

or the theme…?

May be. To find out, try switching to the unedited default, core-bundled Theme (such as Twenty Twelve, Twenty Thirteen or Twenty Fourteen) for a moment using the WP dashboard to rule out any theme-specific issue.

or a plugin?

May be. To find out, try:
– deactivating ALL plugins temporarily to see if this resolves the problem. If this works, re-activate them individually (one-by-one) to find the problematic plugin(s).
– resetting the plugins folder by FTP or PhpMyAdmin. Sometimes, an apparently inactive plugin can still cause problems (because the hooks remain unless plugins completely removed or some plugins stick around in cached files. So by renaming the folder, you break them and force them inactive).