So it appears that you are migrating the instance to another server and this instance is working as a publisher, distributor and subscriber (at least this is what I am guessing from your short explanation).
- Backup your publisher and subscriber databases.
- Restore them on the destination instance with norecovery and setup log shipping or mirroring between the two servers.
- At this time the replication is intact and there is no downtime been taken i.e. your application is still up and running.
- Take the downtime
- Remove LS or mirroring from the target instance after ensuring that the source and destination DBs are in sync.
- Take the last log backup of subscriber and publisher databases and restore them on the target databases with recovery.
- Setup the distribution and publication on the new instance.
- Setup replication between the publisher DB and whatever subscribers you have but do not initialize them as the data is in sync already.
- Do the same with the subscriber database.
- Change the connection strings in the application to point to the new server.