You have a few options, depending on how much you're willing to
spend:
1. Easiest and most convenient method, drop by any Caesars
outlet (PlazaSing/Raffles) and get a bottle of sword oil. = $8.
It's basically some petrochemical distillate, judging from the
smell. I kinda dislike the smell though.
2. The more traditional method: Buy Choji oil, this oil is
traditionally used by the Japanese to oil their katanas. However,
high quality choji oil is very very expensive. You will know that
when you try purchasing them online.
3. Make your OWN choji oil! XD It can be done rather simply, a
few of the Singapore Sword collectors are doing it. Basically, 99%
mineral oil + 1% clove oil and shake! Shouldn't cost you more than
$15 total.
PS: Using cooking oil, baby oil, petrol...will leave too thick
an oil coat on your blade...they will damage it overtime because
those oils might have reactive ingredients in them. Eg. cooking oil
can turn rancid overtime and eventually become acidic.
Hope that helps. Cheers! BTW, what kind of sword is it? Got any
pictures?