For Asynchronous replication, you can setup bucardo  and run in your local server. The remote or cloud server is not required for any installation but you must have postgres 9.x above for both location, you can setup master-master replication or master-slave replication. Once installed just cron the sync on demand by starting and stopping the service.  Bucardo 5.1.1 works for me hope it can help you too.

Forget asynchronous replication. Suppose you have two databases asynchronous replicated, each accessed by one diferent user. In a time when the two dates are not connected, the two users insert a new record in the same object in each of the two databases (in sale.order for example). I have the same ID for sale.order? (Primary key IDs are serial long in odoo). Also reference field will have the same SO ...? Raise this situation a conflict at next replication ? I think yes...

Hi Paulo
For your problem, i think you can get a good result if you define a cron job which synchronise data on the two databases periodically.

A link for definition of cron job : http://www.thesitewizard.com/general/set-cron-job.shtml

Best regards
NB: If my answer help you, don't forget to vote my message. Thank you.

Please check this:

http://www.rubyrep.org/

U can find everthing what is important.

Lets say if your internet connection goes off at your Local Office. The people who are using at your office will prepare some quotes in local erp and you might be travelling and might make quotations on cloud database,

How does above mentioned solutions help? Does it take care of conflicts too?

Read this.

It'll help you with setting up a multi master or master slave replication for Odoo

One easy practical solution is to backup your database in cloud drive, like dropbox. So syncronization process is handle by the cloud drive. What you have to focus is the backup/restore database script which can be triggered by cron/scheduled job.