Really feels unsafe, but neither me nor the computer have suffered any serious injuries yet.

That's due to interference suppression capacitor in the PSU. The safety standard puts the "touch current" limit at something like 300uA (0.3mA), which is definitely in "painful but not dangerous" territory. You do need to exercise caution when plugging in other devices that are also connected to the mains, since that amount of current and voltage can certainly damage sensitive electronics.

Old but good page on such measurements: http://www.aplomb.nl/SMPS_leakage/Doc_ie.html