How can molecule of a few angstroms absorb visible light of a few hundred nanometers? I guess visible light is visible, because it has the right wavelength to be absorbed (or not) and emitted (or not) by many different molecules. Now visible light has a wavelength in the order of a few hundreds nanometers, while the typical size of a molecule is rather in the order of a few angstrom.
I guess the difference between the energy levels of the molecules will have the right magnitude that corresponds to the energy carried by a single photon. But it's still slightly strange, because a classical antenna would need a length of a quarter wavelength to be most effective at absorbing or emitting energy.
I also wonder what the effective size of the scattering cross-section of a molecule to absorb a photon of an appropriate wavelength will be. Is it more in the order of the size of the molecule, or more in the order of the geometric mean between the wavelength and the size of the molecule?
 A: In quantum mechanics you calculate the charge density by taking the square of the wave function. If you do this for a hydrogen atom in a superposition of the ground state the first excited state (1s and 2p) you get an oscillating charge density. If you analyze this oscillating charge using Maxwell's equations, you get all the properties of the hydrogen atom: the absorption, the emission, the line-width...you name it. Everything the atom does in its normal interactions with light makes sense according to Maxwell's equations. 
In quantum mechanics if you have a slab of material made of atoms, then at any given temperature there is a wave function made up of the superposition of the different thermal states of the slab. If you square the amplitude of this wave function you get a time-varying charge density full of oscillations. If you use Maxwell's equations and treat these oscillations as classical antennas, you will obtain the correct black-body spectrum for the solid slab. All the thermal properties of matter in its interaction with radiation (including the photo-electric effect) are consistent with Maxwell's equations. 
It is true that the quantum oscillator is hundreds or thousands of times smaller than the quarter-wave dipole which is the most efficient classical absorber. But you can make a classical antenna shorter by adding an inductance. In an atom, the mass of the electron is the parameter which effectively increases the apparent inductance of the atomic antenna. The only difference with classical antennas is that you cannot normally get such a small size-to-wavelength ration because of the high resistance of copper. 
The reason physicists don't talk about this is that they have a poor understanding of classical antenna theory. I explain how this works in more detail in a series of blog posts starting here: 
A: I'm assuming you're talking about absorbtion lines. In that case it's a mistake to compare the size of the molecule to the wavelength of the photon. These absorption lines appear as a result of the electron energy levels of the molecule in question. These span a range of energies that, for most gases, will usually include visible light. Let's take a look at the Hydrogen atom as an example (a more realistic treatment would look at Hydrogen molecules, not atoms, but this doesn't substantially change the orders of magnitude involved) :
The transition from the second balmer line to the ninth represents an energy change equal to the energy of a violet photon (383 nm), whereas a transition from the second to the third balmer line corresponds to a red photon (656 nm).
As you rightfully point out, what matters is the energy levels that can be excited in your system. Comparison with molecular size are not useful, as the physics involved here is simply not the same as that of antennae.
A: The absorption/radiation mechanism for antenna is purely classical. It depends on the current oscillation on the structure. For a molecule or atom, it is purely quantum. What only matters is energy level difference. There's no direct relation with the size of the particle. 
However, the two mechanisms are not unrelated. They get connected for the case of nanostructures, e.g., nano antennas. There the size dependence is not exactly like that for a microwave antenna, but has important effects on absorption. On the other hand, typical plasmonic nano antennas can be understood in terms of collective excitations, which are coherent combinations of electron-hole transitions, so related to energy level spectrum of the many-body electron system. 
A: It is also important to note here the difference between a single molecule or atom and a solid comprised thereof.  A single atom is indeed not terribly likely to absorb a photon - a large bulk of atoms or molecules in a solid, however, is quite a different thing.  The branch of physics that deals with this is called Solid State Physics.  A relevant topic here is the electronic band structure of the solid.  
When tightly packed together, the atomic or molecular orbitals of adjacent members of the solid can overlap and interact, generating a macroscopic electronic structure that extends throughout the solid.  This, in part, is what gives rise to the optical absorption characteristics of solids.
A: Even classically the ability of an antenna to radiate or absorb is not related to its size but to it being "resonant" with the "ether" being its loading impedance. The size is related to the bandwidth over which this resonance can be achieved. For an antenna whose characteristic size is much less than a wavelength the relative bandwidth over which it can radiate reduces exponentially with that size. Think of a Hertzian dipole that is oscillating at one frequency, and there it radiates beautifully. Your cellphone antenna that is much smaller than 15cm (half wavelength at 2GHz) is made resonant with lossy matching circuits on the board over the band of interest, a lousy and inefficient radiator but a radiator, nevertheless. See, the classic results of J. L. Chu "Physical Limitations of Omni-Directional Antennas", JOURNAL OF APPLIED PHYSICS, vol. 19, December 1948, Figs: 5 & 6
A: This is a fun question!
Concerning the cross section for absorption of resonant light.
I can speak to the case of Rubidium atoms and the 780 and 795 nm 
5P doublet.
The cross section is greater than the atomic size, and also greater 
than the mean of the wavelength and atom size.  In fact it's much nearer to the wavelength of the light!  The experiment is fairly easy.  You look at the transmission of resonant light through a cell with Rb as a function of temperature.  (The vapor density of Rb is a strong function of temperature.)   
