With incoming and outgoing email servers, you can make emails sent to your company catchall account automatically flow directly into Odoo to the appropriate record.
However, what about emails that go directly to your individual work email address that are not captured automatically by Odoo? Odoo has an app for that.

Simply navigate to Gmail, click Get Add-ons, and then search Odoo.
Click install. If you are a google admin, you can click admin install to install the app across all users within the organization.
A new Odoo icon shows on the right panel in Gmail. This is the Odoo Gmail plugin.
Click on any individual email and click on the Odoo addon. Now click Grant Permission.
Authenticate with Gmail.
Now click Login
Specify your database URL. E.g. bizylife.odoo.com
Then click login. It will prompt you saying "Let Gmail access your Odoo database?" Click Allow.
Refresh your browser and the system should now tell you if a contact already exists in your database and if so, any linked opportunities, tickets, or tasks with the associated contact. You can also create new contacts, opportunities, tickets, and tasks directly from here. The system will also automatically attempt to enrich these contacts. As a disclaimer, contact enrichment consumes Odoo IAP credits which are purchased directly from Odoo.
Hope this helps and let us know if you have any issues.
Integrating Odoo with Gmail Plugin