To pour oil (literally) — to add liquid oil to something, e.g. when cooking or lubricating machinery.
天ぷらを揚げる前に鍋に油を注ぐ。
Before frying tempura, pour oil into the pot.
古い自転車のチェーンに油を注ぐと音が静かになる。
If you oil the chain of an old bicycle, the noise quiets down.
ランプに油を注ぐ役目は彼の仕事だった。
It was his job to pour oil into the lamp.
To add fuel to the fire (figuratively) — to exacerbate a dispute or inflame emotions; to encourage escalation.
彼の一言がさらに火に油を注いだ。
His one remark only added fuel to the fire.
相手を非難するだけでは事態に油を注ぐことになる。
Simply blaming the other side will only add fuel to the situation.
冷静に話し合わないと、外野の意見が油を注ぐことになる。
If you don't talk calmly, outside opinions will only add fuel to the fire.