Exim error SMTP call from [X.X.X.X]:50135 dropped: too many syntax or protocol error

Fix your mailserver, ensure you don't make faulty setup again that will allow relaying. I advise you to check own mails for spam too to ensure some of your own users don't spam either deliberately or if their mail account gets stolen and thief uses it to legitimately tries to spam from your server.

When that is done, change the ip of your mailserver to other IP available, adjust DNS records, to reflect the IP change.

You can force that mails are sent from other IP with SNAT rule in iptables

iptables -t nat -D POSTROUTING -j SNAT -p tcp --dport 25 --to ot.her.ip.address

extra: add SPF field in zone that will confirm new IP is legit source to send mails for domain(s) Add DKIM filter to sign mails.

oh, and If I may suggest to try replacing exim with postfix

To fix this get a new IP address for your outbound mail server ASAP. Remember to also realign reverse dns for the IP address. Also continue on with the blacklist removals. If you cannot get an external IP consider a 3rd party mail filtering service or a gateway.

As a follow up, don't send mail directly from exchange out to the internet. If possibly put in a secondary mail gateway that will allow you to better manage your outbound emails. You can set this up very easily if you have a bit of linux experience, and also you can keep a good record of who is using your email server for what. You could also do this by enabling SMTP logging on the SMTP virtual server in exchange, but I find even this log to be a bit of a pain to get accurate measurements for.

If you cannot use a gateway, even if just as a temporary measure use an external provider such as postini or message labs. http://www.google.com/postini/index.html