Do the burls extend all the way around the section of log, or are they just on one side.  Second, what would you like to make from the burl wood?

I've only had one burl to work with, several years ago.  My understanding is that the burl figure does not extend into the section of log.  Imagine if you will a ball of pie dough that gets thrown onto the side of a log, deforms, and sticks.  There would not be bark between the log and burl as in this analogy, but the burl figure would only be in the deformed pie dough, if that makes any sense.  Maybe on a burl that grew for several decades some of the burl figure extends into the log?

There can be voids in burls.  Seems like I've seen pictures here of turned bowl burls that were wrapped in shrink wrap after the outside was turned and the tenon grabbed in a 4 jaw chuck, because of voids.

First off get then in plastic so they don't crack if they haven't already.

Without seeing them its hard to give advice, a picture would help.

Ron Sardo wrote on Dec 29^th, 2016 at 7:52am:

+1

Although you said it was burl (inconsistent grain direction) this may help you to determine what shape or style you want.
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Thanks guys haven't had Time to snap a pic. When prep is mentioned with plastic wrap? What does that do? Kinda novice here? Does it retain the moisture so it doesn't dry out? I cut some nice red cedar this past spring and sure enough they cracked. Assuming from drying out.... yikes

I would paint the cut, raw wood areas with a product called Anchorseal, or lacking that, a couple of coats of cheap latex paint.
You, ideally, want to regulate the drying process, slow it down some.
Most of the moisture escapes wood through the end grain...But with a Burl, end grain could be anywhere, or everywhere, so it is best to paint anywhere the wood was cut.
Keep the paint off the bark as much as you can because you might 'use' the bark as a feature.
Store the burl out of the sun, and somewhere with a cool, stable environment until you get around to it.

I would cut chunks off in a size I could handle on the lathe, and try to get as much out of it as I could...down to pen blanks.