Unfortunately, radio signals, even strong ones are quite common in the universe. Many things, including the sun, emit light in the radio band.
An example of a strong radio signal that is naturally produced is a pulsar. When pulsars were discovered (by Jocelyn Bell), they thought the signals were from extraterrestrials because they were regularly repeating.

The reason they use mathematical constants and such is because anybody searching for us will be looking for patterns in the signals. The only patterns we can be relatively sure they will recognize are those based on physics or mathematics. Anything else (like religious or cultural messages) would probably be gibberish to them. As for the intelligence question, I think we would qualify as intelligent any creature that would recognize the signifigance of our signals. Of course, we would recognize the signifigance such a signal and many think that humans are not particularly intelligent, so I'll leave that matter up to you.