its possible. the biggest issue I see is getting the color to match.. paint stores have many versions of oak like dozens. your best bet is get small testers and test it on a piece of pine to get it close it may take a few coats to get it where it looks ok. besides that staining is pretty straight forward. clean the cabinets well using a vacuum and a tack cloth to remove ALL the dust take the cabinets to a garage of somewhere that wind wont affect the process. and use light coats dont just slop it on you can always go back and add another coat after it dries. after the color is correct and everything is dry apply a few coats of a polyurethane to protect all your hard work. You can find step by step instructions through Google.

They will never look like oak. You would do better to paint them a color like a semigloss black or even an off white.

you can stain it the same shade but it will still look like pine because of the knots and the way the grain looks

I have two bedside cabinets in pine which I would like to go with the other oak furniture in my bedroom. Can I do this by staining the cabinets? If so is there any prepping I need to do to the cabinets first or any other advice on the process in general? Thanks