I'm using my own root server for my email accounts. All the traffic between my pc and my server is encrypted. Is there a possibility to force my email-server to communicate with other email-servers also encrypted?
Yes, you can tell your mail server that you want it to use encryption when talking to other mail server. Of course, there is always the possibility that the mail server on the other side of the SMTP connection don't want to establish an encrypted connection. Hence you will need to have a policy on whatever to allow the connection to proceed or not in such a case.
The two configuration options you are after are smtp_tls_security_level and smtpd_tls_security_level. smtp_tls_* controls sending while smtpd_tls_* controls receiving.
The usually sensible thing, for Internet wide e-mail, is to allow for opportunistic encryption. That translates into the config value may.
Only if they support SSL as well.
I assume from the tag you are using postfix. There is an option in main.cf for that:
You can have it verify certificates or not, or use SSL when available but still send email when it isn't. Keep in mind that requiring encryption will make any mail you send to sites that do not support SSL undeliverable, and requiring valid certificates will make mail undeliverable from your site to those with self-signed certificates.
Here is the documentation for that option: http://www.postfix.org/postconf.5.html#smtp_tls_security_level