Not getting contact details
There's usually a lot of parties involved in the interview process. It wouldn't be uncommon that the person you interviewed with isn't the person you will be in contact with afterwards, or maybe this person just doesn't have these details on hand. They may not even know the contact details of said person, or know who that person is, for that matter (the person who normally deals with this might be on leave or going on leave, this person might be new to interviewing people, there may be a few people who may follow up on this, or some other reason).
They could just give you a general email address of the company, but this information is often publicly accessible, or it would simply be easier to have the secretary give you a business card containing this information afterwards than have someone write it down somewhere during the interview.
Let's add to this the fact that companies usually contact candidates, not the other way around.
Now the hesitance to give out some contact details doesn't seem so strange.
On the way out I passed by the secretary to ask for contact information and she said just use whatever e-mail address I had used to apply.
If you accurately described what happened, you are definitely partly to blame. During the interview, they said you should get the details on the way out. You made an attempt to do so by asking the secretary, who assumed that you already had this information - perhaps not a great assumption, given that you just asked for it (perhaps your phrasing was unclear), but you should've simply said "I don't have an e-mail address for the company, I didn't apply using e-mail", or whatever.
Not getting an email or voice message
Some people prefer phone calls over other forms of communication. Some people don't like to leave messages. That's simply the way it goes sometimes. You could perhaps see them wanting to tell you over the phone as a sign of respect, although the actual reason is anyone's guess.
Another alternative is that you were still being considered, and they wanted to find out what you thought of the interview and them (over the phone) before arranging a second interview - the inability to get hold of you may just have led them to no longer consider you.
Playing 'phone tag'
How reachable you are during office hours and when you tried to contact them may have come into play here - repeated failed attempts at getting hold of you may indicate that you're difficult to get hold of, in general, and, if you tried to call them back outside office hours, their lack of reachability could certainly make sense. Your scenario may be different though, I'm just putting this out there as a possibility. Just being out of sync with someone is also a possibility.
Getting the "we gave the job to someone else" response
You may have come across as still interested, in which case saying that they gave the job to someone else is an expected response. The person on the other side may simply prepared to say they gave the job to someone else, and didn't let the fact that you appeared to no longer be interested deter them from doing so. They may have simply wanted to make it clear, just in case. But anyway, there are enough possibilities that I wouldn't see it as particularly rude.
Everything you encountered is certainly explainable in a way that doesn't leave the interviewing company at fault.
Also remember to think of the company as a company, not an individual. There are often communication gaps, people on leave, people not acting professionally, etc. in any company that you shouldn't hold your experience during the interview process against the company as a whole (although my guess is that, more often than not, your experience during the interview process should give you a decent idea of the company).
Whether you choose to give the company the benefit of the doubt, or end up thinking they're totally unprofessional and it's definitely not a place you want to work for this reason, is completely up to you.