That's not an odd situation. That's a common situation. I'm sure there are people here who haven't been in that situation, but most of us have. Some employers mean that when they say it. Others just say it to try to keep people on the hook in case the new people they just hired don't work out.
If you're serious about getting a job, rather than just applying at one place and hope for the best, apply more places. Before I got my first job in my industry, I went from applying to just a few companies here and there, after I did some research on them, and using one resume site that promised all the job bites I could want, to applying to several places a day and using numerous resume boards.
I will admit that I had a lot of places to tell I wasn't interested any longer after I did finally get a job, but that's a better problem to have than working a part time summer job quality job with a degree and the student loans to go with it.
When you get a call from a company saying they're interested in you as a potential new hire, it's certainly worthwhile spending some time to learn about their company. Find out what they do, if you need to, come up with some questions to ask about their business that would be pertinent to your job there - because if they interview you, they should have a point where they let you ask questions about them, and you should have some, to show some interest. Once you have that, but you have this interview in a little bit? Apply somewhere else, don't count on the interview getting you a job.
You can stop worrying about getting a job when you have a written offer letter in hand. An email on the computer that they want you to sign and return saying you've accepted the job is good enough. A statement telling you they're going to send it isn't enough. It took several potential employers promising they were going to send me an offer letter and then weeks went by without it arriving to clue me in. But talking with other people, that happens a lot, too.
It's still good to keep a good idea of what companies might be still actively interested, and it's certainly a good idea to try to keep them straight, especially if you're applying at different companies that directly compete with each other. Few workers can afford to be completely set on one company, but most employers seem to like to maintain the illusion that they're more exciting to work for than their competition.