Tracing MX records to its mail server

Dear Experts,
2 part question. I am trying to assist a poetential client of ours with his email. I used a DNS query to try and find his MX records. I typed in his internet domain name and his name server. Nothing comes up. The strange part is, he is using email addresses with his internet domain name, e.x. name@domainname.com but his in going and out going is a private IP address. My problem is that i cannot find where his MX records are sitting? I am also mystified on how he is even able to use his email? Although, he does complain of sending an email out and getting a response "unknown host" but an hour later resending the same email and it goes through...Unfortunately my client has no idea either.-------I ran the DNS Query from 2 external locations and not on his network and there is no domain name found. I already went to dnsstuff and i found a name server. But the name server is strange as it reads, BLACKHOLE-1.IANA.ORG. I repeated the DNS query and was left with nothing still. The problem is that I nor my client knows how to set this up or fix this on his internal server. I need step by step instructions or advice. I do not have access to his Server.