Do different vibrational modes correspond to vibrational energy levels?
yes and no: all vibrational normal modes have a different energy (with the proviso that some may be accidentally degenerate) and hence different absorption frequency. (Fundamental frequencies have vibrational transitions that occur with selection rule $\Delta n=\pm 1$.) All normal modes exist in their ground state with zero point energy (quantum number $n=0$) as well as in other levels based on the same mode ($n&gt;0$) which are populated according the Boltzmann distribution at temperature T. Thus each basic vibrational mode i has its own stack of energy levels, with quantum numbers $n= 0, 1, 2 \cdot\cdot$ and (harmonic oscillator) energy $E_i=\nu_i(n_i+1/2)$ with quantum numbers $n_i$ and frequency $\nu_i$ in  $\pu {cm^{-1}}$. The total zero point energy of the molecule is the sum of all the individual zero point energies above the zero of energy.

The number of vibrational levels populated at a given temperature depends on the vibrational level spacing, thus low frequency modes, say, $500 \pu{cm^{-1}}$ have far more levels populated than a high frequency, say $1500 \pu{cm^{-1}}$ mode. 

As the energy increases the number of vibrational energy levels / unit energy can become very large indeed in polyatomic molecules. There are overtones where only one vibrational mode is excited, but with more than one quantum of energy, and combinations where two or more different vibrations of different frequency are excited and so each have non zero quantum numbers. 

In water molecules there are 3 vibrations (of frequency approx $3650,1595, 3756 \pu{cm^{-1}}$) if we label them in order with quantum numbers then [000] is the zero point energy $(3650+1595+3756)/2=4500 \pu{cm^{-1}}$,  [010] a fundamental in the second frequency and [020] an overtone in this mode and [110] a combination of modes 1 and 2 with energy above zero of $4500+3650+1595 \pu{cm^{-1}}$