Need help identifying cause and resolving TLS errors in Exim relay server

We run a relay server for member schools to provide initial filtering before passing on to each school. Our server currently has self signed certificates (not sure if that is the cause of my errors). We are getting many errors like the following in our mail log:

2015-09-24 09:19:08 TLS error on connection from (na01-bn1-obe.outbound.protection.outlook.com) [157.56.110.86] (SSL_accept): error:1408A0C1:SSL routines:SSL3_GET_CLIENT_HELLO:no shared cipher
2015-09-24 09:19:08 TLS client disconnected cleanly (rejected our certificate?)
2015-09-24 09:19:08 DNS list lookup defer (probably timeout) for savingworktocloud.com.rbl.baruwa.net: assumed not in list
2015-09-24 09:19:08 TLS error on connection from (na01-bn1-obe.outbound.protection.outlook.com) [157.56.110.65] (SSL_accept): error:1408A0C1:SSL routines:SSL3_GET_CLIENT_HELLO:no shared cipher
2015-09-24 09:19:08 TLS client disconnected cleanly (rejected our certificate?)
2015-09-24 09:19:09 DNS list lookup defer (probably timeout) for 226.20.89.69.rbl.baruwa.net: assumed not in list

Running grep shows the following:

grep ciphers /etc/exim/exim.conf
tls_require_ciphers = TLSv1+HIGH : !SSLv2 : RC4+MEDIUM : !aNULL : !eNULL : !3DES : !MD5 : !AES : !CAMELLIA : !PSK : !KRB5 : @STRENGTH


What steps would I need to take to eliminate these errors.
tamray_techAsked:
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btanExec ConsultantCommented:
Your client should provide the reason. If not, connect using the
Better to use OpenSSL s_client to determine further reason via testing the command to the exim smtp server, such as :  openssl s_client -connect $your_ip:$your port
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tamray_techAuthor Commented:
I found the reason for the errors come from mail servers wanting to connect via sslv3, which we do not support, because of vulnerabilities. I am not clear if that means the message will never be delivered or if it will renegotiate with a different cipher. Any ideas how best to resolve the problem?
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tamray_techAuthor Commented:
Resolved it by adding the following to exim.conf

openssl_options = +no_sslv2 +no_sslv3

completely disables sslv3
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tamray_techAuthor Commented:
I've requested that this question be closed as follows:

Accepted answer: 0 points for tamray_tech's comment #a41003686

for the following reason:

Resolved issue
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btanExec ConsultantCommented:
Yes - you can also see this if exim pertaining to Poodle is in openssl
To disable SSLv3 in Exim when compiled with OpenSSL, set the following in
the main options section of your configuration file. It affects both
incoming and outgoing connections.

        openssl_options = +no_sslv2 +no_sslv3
https://lists.exim.org/lurker/message/20141017.093614.e5c38176.en.html

For the GnuTLS case if that is used to compiled, it is also possible to completely disable SSLv3 support on these service ports with the following cipher list:

ALL:!ADH:+HIGH:+MEDIUM:-LOW:-SSLv2:-SSLv3:-EXP

But do note that for all above, completely disabling SSLv3 ciphers on the above service ports greatly limits browser compatibility and prevents connections from all but a few modern browsers such as Google Chrome.
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