You are not very specific, but it seems you may be looking for Postgresql streaming replication?  The master server continuously replicates to a slave server. If there is no internet it keeps a log of transactions until it can re-connect. You need to make sure that you allocate a big enough log size depending on your database load and duration of 'no-internet' periods.  There are plenty of tutorials about that.

Obviously the slave is a read only replica.  Odoo isn't really made to run on a read-only database so you can't use it to 'view' Odoo data (by using Odoo)

If that doesn't suit you, you may want to look into multi-master replication but i do not know the details or the quality of the solutions.