I'm fairly sure the lore on Portal Storms indicate that it causes random teleportation events, and that we saw them spreading Xen wildlife throughout the first game before HL2 named them. Gordon and Alyx were probably lucky not to have been teleported to god knows where in Episode 2. This is probably why Xen is such a difficult place to live; it's probably wracked with portal storms shoofing you to another island when you least expect it. On the other hands, that's probably how life propagates across the floating islands without flight.
Yes, the headcrabs, bullsquids, houndeyes etc that teleport in are part of the portal storms caused by the resonance cascade, separate from those Xen military units teleported directly to Earth by the Nihilanth.
The portal storms were indeed quite unpredictable and chaotic, however, analysis of previous major events have revealed that the storms themselves almost exclusively acted in one direction, with the aliens from Xen teleporting to Earth, but not very commonly the other way around. As for portal storms post Combine-occupation: it appears that the Combine themselves have a level of control over the appearance of these storms. I wouldn't be surprised if the world-wide portal storms previous to their arrival were a direct result of their forces opening a rift between their dimension and ours. Either way, stray portal activity nowadays is at a minimum, being barely registrable on any of my equipment!