What exactly is a 'solution' in string theory? Is it a spacetime metric of some sort or the terms of a S-matrix of some sort?

We have a non-peturbative definition of M-theory and string theories on AdS Space through the AdS/.CFT correspondence. Now, these are 10 or 11-dimensional. To get rid of the extra 6 or 7 dimensions, you need to compactify it on a 6-dimensional or 7-dimensional manifold.

A particularly convinient compactifications of 11-dimensional M-theory is on $G(2)$-holonomy manifolds. Particularly convinient compactifications of 10-dimensional string theories, such as Type HE, are on $SU(3)$-holonomy Calabi-Yau manifolds. Of course, it's not necessary; e.g. if the world happens to be something with $\mathcal N=2$ supersymmetry, as opposed to $\mathcal N=1$.

Why are there so many 'solutions'?

Because there are *lots* of these manifolds!

I thought string theory was supposed to be finite, why do perturbative series still diverge?

Uh... Yes. But it's renormaliable. And there **are** non-peturbative definitions in AdS spacetime.

Is there any experimental technique to limit the number of 'solutions'? Will experimental techniques be able to pinpoint a solution within present day string theorists' life times too? If not, how long will it take before we can experimentally probe these things?

In principle, it's possible. But in anyone's lifetime... Do you know how big $10^{500} $ is? % See this.

Are string theorists completely relaxed about these issues? Or are they in anguish?

There's the branch of String Phenomenology that attempts to find the correct vacua...

This post imported from StackExchange Physics at 2014-03-07 16:38 (UCT), posted by SE-user Dimensio1n0