Why is Diiron nonacarbonyl so exceptional?
Wikipedia (primary reference) suggests a possible reason for $\ce{Fe2(CO)9}$ dissolving preferentially in THF versus nonpolar solvents:  it reacts according to the scheme

$\ce{Fe2(CO)9 + THF &lt;=&gt; Fe(CO)5 + Fe(CO)4 \cdot THF}$

Such a reaction is invoked to account for the dinuclear complex giving mononuclear products with various ligands in THF.  A similar reaction with the corresponding cobalt and manganese species would have to produce radical or ionic products, due to the odd atomic number of the metal, and so would be less favored.

This would not, of course, explain the lack of solubility in nonpolar solvents or nonvolatility of $\ce{Fe2(CO)9}$.  It is possible, however, that the same $\ce{Fe2(CO)9}$ molecules that bind with the oxygen in THF could also bind intermolecularly through the oxygen atoms, in effect delocalizing the covalent bonding and creating more intermolecular cohesion.

We can represent this type of interaction using the SMILES structural notation.  Fr a single $\ce{Fe2(CO)9}$ molecule it would look like this, taken from Wikipedia:

$\ce{O=C1[Fe]2(=C=O)(=C=O)(=C=O)C(=O)[Fe]1(=C=O)(=C=O)(=C=O)C2=O}$

For two molecules we would have

$\ce{[O=C1[Fe]2(=C=O)(=C=O)(=C=O)C(=O)[Fe]1(=C=O)(=C=O)(=C=O)C2=O][O=C1[Fe]2(=C=O)(=C=O)(=C=O)C(=O)[Fe]1(=C=O)(=C=O)(=C=O)C2=O]}$

Then we have a contributing structure where an oxygen atom from the left molecule could combine with the right one, displacing an iron pentacarbonyl molecule:

$\ce{[O=C1[Fe]2(=C=O)(=C=O)(=C=O)C(=O)[Fe]1(=C=O)(=C=O)(=C=O)C2=\color{blue}{O[Fe]}(=C=O)(=C=O)(=C=O)C=O][[Fe](=C=O)(=C=O)(=C=O)(=C=O)C=O]}$

where the blue atoms form an intermolecular bond in this contributing structure.  The displaced iron pentacarbonyl molecule is in the last set of brackets.

The Case of Hydrogen Bonding

The delocalization of covalent bonds, hypothesized above, may be seen in a more familiar context:  hydrogen bonding.  Usually thus is rendered as an electrostatic attraction between oppositely charged atoms.  But it may also be considered as a molecular-orbital interaction:  a nonbonding electron pair overlaps an adjacent molecule's antibonding orbital in exchange for creating an "intermolecular" covalent bond.  With water it would look like this

$\ce{[HOH][HOH]}$

with the hydrogen-bonded, "intermolecular bonded" contribution

$\ce{[H\color{blue}{O}(H)\color{blue}{H}^+][OH^-]}$

where the intermolecular bond is between the blue atoms.  This is also the autoionized structure for water.