There are a few different things at play here, but generally speaking: yes, a nucleus of ununoctium is larger than a nucleus of Sodium, and no, the electron orbitals of Ununoctium may not be larger than those in Sodium.
On a nuclear level, protons and neutrons do take up a finite amount of space. The size of the nucleus is partially determined by the number of protons and neutrons, but also by the binding energy of the nucleus (in other words, how energetically favorable the formation of that nucleus is).
Neon atomic orbitals
One measure of this is the energy of the first excited state in the nucleus: if the first excited state is very high in energy, it means the ground state is very well bound, and the nucleus is probably smaller than its nearby neighbors on the chart of the nuclides.
At the atomic (electron orbital) level, the more electrons an atom has, the more diffuse they have to be due to charge repulsion and the Pauli exclusion principle. However, the closure of a valence orbital can make a huge difference. Thus, an atom of cesium is larger than an atom of sodium, but an atom of chlorine is actually smaller than the sodium atom.
Two basic trends are apparent across the periodic table: atomic radius increases as you move down a column, and decreases as you move across a row. Sodium has a pretty big atomic radius because of that one valence electron; ununoctium, being in the same period as a noble gas, will likely have a closed valence shell (we don't know for sure yet!), meaning its atomic radius could very well be smaller than sodium's.
One useful thing to consider is that the size of the nucleus is orders of magnitude smaller than the size of the atom: 10-15 meters versus 10-10 meters. So even as the nucleus expands with increasing proton and neutron number, it has more than enough space to expand into without ever affecting the electrons!
Kelly Chipps (AKA nuclear.kelly)
Department of Physics
Colorado School of Mines
Kimberly Lane from Billings, MT