Peter,
Unfortunately this sticky stuff is the degradation of the material and is currently irreversible. It's called plasticizer migration.
Different plastics/rubber/etc. have different needs and talking to a conservator to identify what materials you have would be a good step--some of them could potentially require quarantine from other objects in your collection. However, if you don't have the means to do that at this time, you can slow the process by making sure the objects are in a cold, dust-free, and dark location. Always use gloves and don't use any liquids on them.
I'm not a conservator, but the collection I deal with has LOTS of plastic and I've seen sticky in various forms, some not so pretty!
Book to read: "Conservation of Plastics" by Yvonne Shashoua
Video to watch from Connecting to Collections: http://www.connectingtocollections.org/online-event-recordings-care-of-plastics/
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Stacey Swigart
Curator, Collections
Please Touch Museum
Philadelphia PA
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