Probably the best you'll get, dead fall, and I would take it if its not punked out, soft and decaying, that would burn but take a while to dry, unless you can bring it inside, could have insects, so if its that far gone, its not worth the hassle.
Many dead standing I have found are worth processing, dead elm is one, and you may find it in varying condition, trunk partially punked, top hard and dry, brittle, may dull your saw chain a little sooner, but well worth grabbing. Most times it cuts easily, and some of these elm trees will provide a lot of wood. Partially punked elm is ok, if there is no solid wood in it, but its standing, it can be used, but if its saturated it, and has to be dried outside, not worth it. Once dry it may burn like poplar or similar softwood, quickly and hot.
I've been in the same situation and I find that with enough room around my stove, I can easily dry out standing dead trees once processed.
You may want to consider mixing this with your dry wood, cut it up, get it under cover bring what you can inside, start the fire with the driest you have, get a bed of coals, then use both dry and less dry, see how much sizzle you get, and do CHECK your flue, and monitor same for creosote. Check the firebox for flame, you don't want a smoldering mess, you need a good yellow flame, so stoke according and mix in dry wood as needed. I've got 1 cord of maple right now, borderline moisture, but bring it in for 24 hours, near the stove, no sizzle. It happens, firewood processing is hard time consuming work for most, and often times it may not get done on time, I'm working on next years now, and some recently cut dead trees with varying moisture for this season, I would have preferred to have it all done but that's how it goes, so you work with it as best you can. I've never had a creosote problem doing the above, sure its more involved but you can make it work. Dead elm will dry down in a reasonable time, and around here is usually the only barkless dead species of tree. Black cherry will dry rapidly, slower outside this time of year, bring it inside, pleasant odor and it will check/dry very quickly. You may want to split any of this smaller or make a mix, small large, I do that with my 4 way wedge as its offset. I have at times used dry pine to help fire the wood that has some moisture to keep the flue temp up and reduce smoke. If you take this tree, say its elm, tops are real dry, use CARE, as those dry limbs, will over fire a stove in no time, and I mean run away over-firing, I have gotten my pipe glowing by making this mistake, use it sparingly and use the damper/air intake to control it, you'll see how much you can use and what to mix it with. Just some thoughts, hopefully of some use, I know the feeling of being short on wood, and have played this game before with no trouble at all.