How do I keep Mod Podge from getting tacky?

Moisture is the culprit if you're allowing the beads to stay separated until they're truly dry and also "cured" (which can take up to a week).

You can just leave the beads in a non-humid area with good air circulation (or in front of a fan) to speed up the drying, or you can do that in a low temp oven which may also "harden" the surface.

Any humidity they're around later though can cause problems at that point as well (possible stickiness or cloudiness in the clear sealer). So it's best to put a final coat of something that's clear and tougher than white glue (decoupage mediums like ModPodge, etc., are just thinned-down permanent white glues) on decoupaged items if you want the most protection. Polyurethane is probably the best solution, and since it's tougher it will also be less scratch-resistant than white glues.

In the polymer clay world, we like to use the water-based (indoor, Gloss, "Diamond") version of the Varathane brand because it's extra tough and also is UV resistant so won't ever yellow, but other kinds of polyurethane should work too (used to be made by Flecto, now by Rustoleum).

You can buy polyurethanes at hardware and home improvement stores, and the Varathane brand at some of those places and smaller hardware stores or online (quart sizes are fairly available and even half-pint sizes are sold online).

Here are some images of what the Varathane I'm referring to looks like if you're interested, but you don't want the gallon size, and you do want the Gloss version--not the SemiGloss):

http://thefloorfinishshop.com/varathane-diamond-fl...

http://www.homedepot.ca/webapp/wcs/stores/servlet/... (this one is probably the newest label)

Those indoor polyurethanes can also be heated to harden them even further (and quicker) if you want... we usually do that on polymer clay if we use a finish at about 200-250 F, for 5-15 min (that's for the polyurethane; paper could take a much higher temp).

I haven't tried ironing the Mod Podge and even dipping it in hot water will resoften the glue, but diluting it with water before applying helps. I used about 60% water and 40% Mod Podge for most of the things I do.

I have heard that people bake their mod Podged items in the oven to get the last bit of moisture out of it. Are your items able to be baked? You could try an experiment first. Try a low temperature setting and use a fan forced oven if you have one over a longer period of time if you are concerned about heating your jewelry items.