Why do nuclei decay so fast and slow?

In a nutshell, atoms decay because they're unstable and radioactive.

Ununoctium (or Oganesson) has an atomic number of 118. That means that there are 118 protons in the nucleus of one atom of Oganesson, and that isn't including the number of neutrons in the nucleus. We'll look at the most stable isotope of Oganesson, $\mathrm{{}^{294}Og}$. The 294 means that there are 294 nucleons, or a total of 294 protons and neutrons in the nucleus. Now, the largest stable isotope of an element known is $\mathrm{{}^{208}Pb}$, or lead-208.

Beyond that many nucleons, the strong nuclear force begins to have trouble holding all those nucleons together. See, normally, we'd think of the nucleus as impossible because the protons (all having a positive charge) would repel each other, because like charges repel. That's the electromagnetic force. But scientists discovered another force, called the strong nuclear force. The strong nuclear force is many times stronger than the electromagnetic force (there's a reason it's called the strong force) but it only operates over very, very small distances. Beyond those distances, the nucleus starts to fall apart. Oganesson and Uranium atoms are both large enough that the strong force can't hold them together anymore.

So now we know why the atoms are unstable and decay (note that there are more complications to this, but this is the general overview of why). But why the difference in decay time? First, let me address one misconception. Quantum mechanics says that we don't know exactly when an atom will decay, or if it will at all, but for a collection of atoms, we can measure the speed of decay in what's called an element's half-life. It's the time required for the body of atoms to be cut in half.

So, to go back to decay time, it's related (as you might expect) again to the size of the nucleus. Generally, isotopes with an atomic number above 101 have a half-life of under a day, and $\mathrm{{}^{294}Og}$ definitely fits that description. (The one exception here is dubnium-268.) No elements with atomic numbers above 82 have stable isotopes. Uranium's atomic number is 92, so it is radioactive, but decays much more slowly than Oganessson for the simple reason that it is smaller.

Interestingly enough, because of reasons not yet completely understood, there may be a sort of "island" of increased stability around atomic numbers 110 to 114. Oganesson is somewhat close to this island, and it's half-life is longer than some predicted values, lending some credibility to the concept. The idea is that elements with a number of nucleons such that they can be arranged into complete shells within the atomic nucleus have a higher average binding energy per nucleon and can therefore be more stable. You can read more about this here and here.

Hope this helps!

Indeed, the range of possible decay times is much, much wider than even the range you've given, as I found out myself recently. It's hard to imagine a physical quantity that varies more!

In a big-picture sense, one way to think about this is the following: radioactive decay can be thought of crudely as a form of quantum tunnelling, where the nucleons tunnel out of the metastable nuclear bound state to escape to free space (and in doing so, make the nucleus completely unstable and fly apart). It turns out quantum tunnelling probabilities generically have an exponential dependence: for example, in a simple tunnelling model the tunnelling time goes as

$$\tau \sim e^{\sqrt{\Delta E}}$$

where $\Delta E$ is the height of the energy barrier keeping the particle from escaping.

The effective height of the barrier for nuclear tunnelling is a complicated problem to solve in detail, but the point is that if you were to imagine that it varies by, say, a factor of 1000x between a stable and unstable nucleus, this becomes a difference in decay time that is a factor of $e^{\sqrt{1000}}=10^{13}$. So this exponential dependence magnifies the range of possible values greatly relative to the range of energy barriers, and independent of the microscopic details pretty much guarantees that the range of decay lifetimes will vary widely.

Why do atoms decay at all?

For the same reason that rocks roll downhill. There is a general tendency for things that are at a high energy level to "fall" to a lower energy level.

In terms of atomic nuclei, the lowest energy per nucleon is iron (Fe-56). Energy can be released by fission of elements heavier than iron and fusion of elements lighter than iron.

From this perspective, the question is not "why do atoms decay" but "why is decay not instantaneous?" This is because intermediate states require higher energy. However, quantum systems can "tunnel" through an energy barrier with some probability: https://en.wikipedia.org/wiki/Quantum_tunnelling#Radioactive_decay

So, Polonium-210 isotopes decay at a higher rate than Uranium-238 isotopes because the energy barrier between the initial state and the decay product state is lower.

At low temperatures, fusion does not happen spontaneously at all because the energy barrier is extremely high (though, presumably spontaneous fusion through quantum tunneling can happen, it just has an extremely low probability). In stars, the energy barrier is much lower because the temperature is very high and the nuclei involved have a lot of kinetic energy that allows them to overcome some of the Coulomb forces that repel them (the main cause of the energy barrier).