Wow.
Even though Detect Magic is a level 0 spell, it is a really powerful one, especially if it is permanently on a subject, basically making it a Supernatural Ability.
A creature with Invisibility cast on it WILL indeed give off a magical aura that will be detected by the character. However, he will have to concentrate for 3 rounds before he can pinpoint the exact location of the invisible creature. Of course, this also means that if the invisible creature moves out of the arc of the detect magic ability (for example, moves behind the caster) he may have to start over again if he doesn't move the arc to cover the invisible creature again.
The same thing goes for illusions. For example, let's assume that the character in question runs into a Permanent Image of a sleeping dragon.
Before the character is within 60' (range of the spell) all he sees is a sleeping dragon, and he will assume it's real unless he does something to interact with the image beyond this range.
Once he gets in range of the detect magic, he will sense a magical aura. The next ROUND, he will sense the number of auras, and their relative strength. In this case, he'd sense ONE aura, of sufficient strength to be a Permanent Image spell. On the third round, he would know that the magical aura that he is detecting is coming from the dragon. At this point he can ALSO make a spellcraft check at 15 + spell level to figure out what school of magic is involved. If he sucessfully made this check, he'd know that this dragon has an illusion spell cast on it.
Now, this doesn't mean he KNOWS the dragon is an illusion, but he knows there's some type of illusion on the dragon, and he knows how powerful the illusion is. From this information, he may be able to deduce that the dragon is a Permanent Image spell, or at least that there is an illusion spell cast on this dragon with the same spell level as Permanent Image.
If he fails to identify the school of magic, all he knows is that the dragon is radiating a magic aura... what it is could be anything.