A lot of this will depend on the appearance of the objects. The portal in particular lends itself to quite a wide variety of design concepts.
Maybe it will be easier to find a sound once a visual design has been more or less decided upon for each object. Here's what I'd suggest for each:
Assigner/de-assigner: archway with a circular emblem at the top, upon which the relevant skill appears. This could have any number of electronic-style sounds, but I definitely like namida's idea of the sounds being equal and opposite, so that the de-assigner's sound is essentially a reverse of the assigner's.
De-neutraliser: an egg-shaped pod big enough for a lemming to step into. I imagine this having a "scanner" sound followed by a microwave-like "ding" - I'd suggest that both of these sounds be fairly soft and un-intrusive, since multiple lems are meant to be able to use the pod and it could get quite noisy.
Portal: my own preference for portal design is some sort of swirling vortex. This sound could be a soft "swoosh" or similar, I'm thinking unpitched white noise essentially. Again though, the sound here depends so much on what is decided upon to be the appearance of the default portal.
Having said all this, maybe the sounds
could come first and the visual appearance be decided upon second. This may result in some interesting designs!