Can you explain the axes of the Bode plot better?
The axes of the Bode plot are log log axes. The x axis is going to have as units the log on base 10 of the frequency considered: if we span \(\omega\) between 0.1 and 10^4, there will be equidistant ticks on the axis corresponding go the log being -1, 0, 1, 2, 3, 4. The way such ticks are labeled is up to you: you can leave the log or write what that corresponds to in \(\omega\), i.e. .1, 1, 10, 100, 1000, 10000. Same reasoning for the y axis, where you will take the log of the modulus of the transfer function you're considering. The important aspect for sketched Bode plots, is that the ticks on your axes should result in lines of correct slope (0, 1, -1, 2, -2) depending on how many poles/zeros were encountered.
Many books use units of dB for the y axis instead of just the log scale. Please see this FAQ for more information.