Are current and voltage orthogonal in a transmission line?
A transmission line can support two waves, one travelling left, one travelling right. For each wave, the voltage and current are always strictly in phase, with the ratio of the line impedance.

When you add the two waves together to get voltages and currents at a particular point on the transmission line, which gets a bit non-intuitive as voltages add but currents subtract, then depending on the position on the line and the characteristics of the terminations, you can get essentially any phase, any ratio.

Some interesting line lengths are


Very short - an open or shorted line behaves like a capacitor or inductor respectively
Multiples of half a wavelength - the ratio is the same at each end
Odd multiples of a quarter wavelength - the most interesting - inverts the ratio at one end through the square of the line impedance - so open becomes short - 25 ohms becomes 100 ohms if the line is 50 ohms