Beta Covariance
is the covariance matrix of your fitted parameters. It can be thought of as a matrix describing out inter-connected your two parameters are with respect to both themselves and each other.
Residual Variance
I believe is a measure of the goodness-of-fit where the smaller the value, the better the fit to your data.
Inverse Condition
is the inverse (1/x) of the condition number. The condition number defines how sensitive your fitted function is to changes in the input.
scipy.odr
is a wrapper around a much older FORTRAN77 package known as ODRPACK. The documentation for ODRPACK can actually be found on on the scipy website. This may help you in understanding what you need to know as it contains the mathematical descriptions of the parameters.