Can half-elves and half-Orcs interbreed with each other and who will be born in this case?
There are no prefab stat blocks for such a half-half-breed in the rules that I'm aware of. So you'll need to come up with something yourself.
If you are a player: Ask your DM. They may even be willing to come up with a custom stat block for your race.
If you are the DM: It's up to you. Your world, your rules. You could use the stat block for either Half-Elf or Half-Orc, or design something in between.
The rules do not explore this in any detail. They are mostly concerned with player characters.
Lore perspective: possibly, up to the DM
The information about what races orcs can breed with in Volo's Guide to Monsters states
The lore of humans depicts orcs as rapacious fiends, intent on coupling with other humanoids to spread their seed far and wide. In truth, orcs mate with non-orcs only when they think such a match will strengthen the tribe. (p. 88) In order to replenish the casualties of their endless warring, orcs breed prodigiously (and they aren't choosy about what they breed with, which is why such creatures as half-orcs and ogrillons are found in the world). (p. 85)
That is about the level of detail you get. The rest is up to the DM to decide. I am not aware of any mention of a character that is the child of a half-orc and a half-elf in published materials. Even if there would be one, this would depend on the setting.
From a lore perspective, elves and orcs originally could not interbreed (1e MM, p. 76), so it is unlikely there would be half-elf-half-orc crossbreeds:
Half-Orcs: As orcs will breed with anything, there are any number of unsavory mongrels with orcish blood, particularly orc-goblins, orc-hobgoblins, and orc-humans. Orcs cannot cross-breed with elves.
Real-world perspective: it depends
D&D is not a physics simulation, and for the same reasons, not a biology simulation. Real world biology of interbreeding is complex. For example, you can get different results for the same two species, depending on who is the father or mother, as seen in ligers and tigons (offspring of lions and tigers).
Generally, only members of the same species can interbreed and breed true, that is, their offspring is fertile too and can reproduce their kind. Being able to cross-breed is largely how a species is defined. It also is possible to have cross-breeds from separate species, called hybrids, but those are often infertile (like a mule, as the child of a male donkey and female horse), or cannot sustainably reproduce their kind.
Since there is no language about half-elves or half-orcs being infertile, this would be an indication that all humanoids are from the same species. But even giants can interbreed with humanoids, for example the game has half-ogres where ogres, which are of creature type giant, mate with humans, orcs, bugbears or hobgoblins, which all are of humanoid type. There is no mention of them being infertile either. Does this mean humanoids and giants belong to the same species? Or are these hybrids? It's not clear.
Fantasy race does not map usefully to earth biology, maybe not unexpected in a world where minotaurs are a real thing.
From a genetics perspective, if they could interbreed, they simply would be half-human-quarter-orc-quarter-elves overall, but assuming they have diploid genomes like humans, for any given gene there could be a different pair of alleles: human/human, human/orc, human/elf, or elf/orc, depending on which of the two alleles for this gene they randomly inherit from each of their two parents.
PC perspective: not as a playable race
Throughout editions, half-elves and half-orcs have required one of their parents to be a human, and the other an elf or orc. So you could not count the result of a half-elf/half-orc interbreeding as a half-elf nor as a half-orc when it comes to playable races, as this creature did not have a pure human and a pure elf or orc as their parent. It thus would not be playable under the rules, as neither of these systems has an elf-orc or half-elf-half-orc character race.
Half-elves, page 38 of the PHB:
Walking in two worlds but truly belonging to neither, half-elves combine what some say are the best qualities of their elf and human parents
Half-orcs, page 41:
orc and human tribes sometimes form alliances, joining forces into a larger horde to the terror of civilized lands nearby. When these alliances are sealed by marriages, half-orcs are born.
Half-Elves, page 42, PHB:
Born heroes and leaders who combine the best features of humans and elves
Half-Orcs (page 14, PHB 2):
Fierce warriors who combine human resolve with orc savagery
Both on p. 18, PHB:
Humans and elves sometimes wed, (...) they leave an enduring legacy: half-elf children.
Half-orcs who live on the frontier live with either human or orc parents
Bonus answer: D&D 1e
Both on page 17, PHB:
Half-elves do not form a race unto themselves, but rather they can be found amongst both elvenkind and men
Orcs are fecund and create many cross-breeds, most of the offspring of such being typically orcish. However, some one-tenth of orc-human mongrels are sufficiently non-orcish to pass for human