Elves generally died out from the main part of Middle-Earth when they left for the Undying Lands, Uruk-Hai were hunted down (I think), not sure about the rest.
In The Hobbit Tolkien suggests that goblins were responsible for inventing modern war machines. He also says that Hobbits used matches, among other anachronisms. There are a number of quirky artifacts from The Hobbit's legacy a children's story initially unrelated to Tolkien's mythology that don't really make sense in light of the rest.
That said, I don't think Tolkien made any concrete statements about what happened after the first few centuries of the Fourth Age outside of The Book of Lost Tales. That was a very early draft of what ultimately became The Silmarillion, and was ostensibly told to a Medieval mariner who found his way to Tol Eressea. However, I think this 'conceit' was largely replaced by the idea that the mythology had been collected and recorded by Bilbo and Frodo and was passed down by Hobbits.
In short, I don't think we can really say anything concrete. There are some hints, but given the inconsistent nature of Tolkien's mythology at different stages of its conception, I would be wary of most of them.
Here are some hints (not necessarily all) -- and for the Elves, Dwarves and Hobbits at least, the sources date from around the 1950s or later:
Elves: those of Middle-earth that didn't pass into the West were destined to fade in the body at some point. Some Elves who died might still refuse Mandos, remaining as spirits; but the faded Elves of Middle-earth were the Lingerers (see Laws And Customs Among The Eldar, Morgoth's Ring).*
Dwarves: the fewness of Dwarf-women is noted at least (Appendix A), along with this factor putting the Dwarven kind in peril when they have no secure dwellings. That isn't much but it arguably offers a factor that might account for a later dwindling anyway.
Hobbits: Tolkien once noted with respect to Hobbit stature: 'The much later dwindling of Hobbits must be due to a change in their state and way of life; they became a fugitive and secret people, (...) driven to refuge in the forest or wilderness: a wandering and poor folk, forgetful of their arts, living a precarious life absorbed in the search for food and fearful of being seen.' (Unfinished Tales, Disaster Of The Gladden Fields, Appendix)
Orcs: I've never really mused on the evidence here. There might be instances of Tolkien arguably speaking to the orcishness that could be found in some Men of his day, rather than what Frodo might have called an orc (although even in Frodo's day certain half-orcs probably blurred the line a bit).
In addition to Eldorion's mention of The hobbit, I do recall Sam saying (which connects to the question of Moria and the Dwarves): 'Moria: I have heard no news. maybe the foretelling about Durin is not for our time. Dark places still need a lot of cleaning up. I guess it will take a lot of trouble and daring deeds yet to root out the evil creatures from the halls of Moria. There are certainly plenty of Orcs left in such places. It is not likely that we shall ever get quite rid of them.' (Epilogue, not used)**
*Are there some Elves still East of the Sea? I like to think so anyway. While perhaps not usually thought of as part of the corpus of Middle-earth, the final version of Tolkien's Trees of Cortirion (published in The Book of Lost Tales I) appears to speak to a relatively 'recent' time at least: it seems to be a description of faded Warwick at some point.
A faded Warwick may be long ago from our perspective, but still the distant future from Frodo's perspective.
** there's an interesting description in Appendix A which, according to Christopher Tolkien, was possibly rejected or simply lost when the Appendices were being prepared for publication. It notes that Durin returned to Moria and there was light again in deep places, and the sound of hammer and harp '... until the world grew old and the Dwarves failed and the days of Durin's race were ended at last.'
This is vague enough, as it arguably should be. In Appendix A it was said of Durin '... but his line never failed, and five times an heir was born in the House so like to his Forefather...' while the genealogy in the same section (on the chart), contains 'Durin VII and Last'.