Re different types of radiation, see this link for details of the electromagnetic spectrum. WiFi is 2.4GHz (2 * 109 waves per second), putting it around the edge of the "microwave" and "radio wave" bars on that diagram.
Also see this NASA link for a good description of the relationship between wavelength and energy. Curie is believed to have died from exposure to high-energy radiation following her work with X-rays. That's the reason hospitals have shielded booths for radiographers, and why they don't give too many X-rays to someone in a short space of time.
For high-power microwave/radio output, the only known effect is heating. Emissions levels in Wifi and phones are set low enough that this is highly unlikely to be significant ("low" really *is* low!).
There *are* people who claim to be electrosensitive - that is, allergic to EM radiation in the same way as you might be allergic to pollen. To date, tests have not shown that they actually are - in other words, they could not report when they were or weren't being exposed to EM radiation. All tests so far have been small-scale studies though, so it isn't completely impossible. The largest study on this so far has just ended and the researchers are checking their data, so we should have a better idea soon.