Mulu is small and remote so do no expect a wide variety of eating options. Most people eat within the park HQ especially if they are staying in the HQ. However a couple of options lie outside the park serving pretty much the same thing: fried noodles or rice. That being said, the food outside the park is cheaper by a few ringgit so if you're on a tight budget then it's worth the five-minute walk outside the park.
Cafe Mulu is the cafe within the park and it serves a variety of Western and Asian food. Prices are relatively expensive; you can get a non-alcoholic drink and a dish of noodles for around 12 ringgit. It's not going to be the best thing you eat but it fills a hole. Breakfast is included in the price if you stay in the park HQ, and this is actually quite substantial. You can choose between pancake, Western breakfast or Asian breakfast which comes with refillable tea or coffee. Packed lunches can be ordered if you are going on an all-day trek.
The two cafes outside the park, Sweet Water and Good Luck Cafe've (that is not a typo -- at least not on my part) serve similar food to Cafe Mulu. Both are tasty but again no gastronomic epiphanies will be found here, although it is worth coming here if you get bored of the cooking style at the park.
There is nothing from stopping you from bringing you own food, and in fact this may be the better option. It'll be cheaper but bear in mind that kitchen facilities are minimal -- actually, there are almost none, within all accommodation only a kettle is provided. We did, however, see some pretty inventive cooking with kettles. Popular food included mashed potato, porridge, pot noodles and macaroni and cheese. Another good tip is to bring lots of water with you as a bottle of water can cost up to five ringgit per two litres at the park shop or cafe. Don't worry about going over your baggage limit as MasWings only charge one ringgit per kilogram you go over.