<p>If a part is wanted to be made the strongest possible, what slicer settings should be used? </p>

<ul>
<li><p>3-5 shells vs  all shells, no infill? </p></li>
<li><p>100% infill vs  some other % infill?</p></li>
<li><p>Thin layer height vs thick layer height?</p></li>
<li><p>Any other relevant settings?</p></li>
</ul>

If your real question is what would be the strongest then I say - the solid would be the strongest - no doubt.
But if the question is:
what be the strongest in comparison to weight or
what is the strongest in comparison to the cost (amount of material)
then these are good questions!
You can of course find many tutorials and comparisons on the net and there will be many answers - which all of them could be good/bad ;)
If these are your questions then instead of simple answer you can ask more questions like:
in which orientation or
for what purpose or
for continues stress or maybe for variable stress or
for bending forces / shearing forces or maybe tearing forces
all these forces and circumstances could require other answer... which could also lead to other questions :)
But according to my experience, the strongest settings (for general purpose) is 3 outlines (and the same number of first/last layers) and triangle infill 20-25 %
Why I think this is the strongest, 3 layers gives good chance to have well stickiness even if there are geometric/design issues and triangle infill gives good (and common) way to carry and spread forces.
But as I said it depends on many input data.
Let's look at these figures:
in figure A we have the strongest composition for compression; this is because all working forces try to damage material particles which is of course hard to do (depending on material density and length of polymers and the way they are tangled and so on - in general - material strength only).
If we consider figure B where forces try to tear apart layers then we know that we base on stickiness between layers which can vary on printing parameters (as is temperature and speed).
Finally, figure C shows shearing forces - in terms of layered structure it doesn't really differ from tearing apart but the results (the resistance of and object) is even weaker - it's because we base on stickiness and we additionally have less effective field of working stickiness) which reduces endurance of an object.