How come a steady stream of oil got repelled by a positively charged glass rod, whereas if water were used instead, it became attracted to the rod all of a sudden? Is it because water is inherently negatively charged and oil is inherently positively charged?
Water is a polar molecule. It has a boomerang shape, with oxygen in the middle, which has a negative charge, and hydrogens at each end, which are positive. The hydrogens are sharing their electrons with the oxygen, but the oxygen is a bit "greedy", so it holds the electrons a bit tighter than the hydrogens do.
When you subject a thin steady stream of water to an electric charge, of either polarity, the water molecules tend to rotate so that their charges are aligned with the external charge, with opposite charges attracting and like charges repelling. So if you bring a positively charged rod near the stream, the negative sides of the water molecules turn towards the rod, and that attracts the stream towards the rod. And conversely, if you bring a negatively charged rod near the stream, the positive sides of the water molecules turn towards the rod, and that also attracts the stream towards the rod.
In contrast, oil molecules are non-polar. They are chains of say 15 to 50 carbon atoms, with hydrogens attached to every carbon. (There may also be a bit of branching in the carbon chain). The hydrogens are on the outside of the chain, so the positive charges of the hydrogen shield the negative charges of the carbons from the outside world. So if you bring a positively charged rod near an oil stream, the stream will be repelled, but it will be attracted by a negatively charged rod.
There are also some differences in behaviour because oil is not electrically conductive, but water is. (Actually, pure water isn't a great conductor, but even small amounts of dissolved salts & minerals increase its conductivity quite a bit).