Do PIC micorcontrollers NEED an external oscillator?

Yes, the 16F84 does need an external oscillator. It is a very old PIC.

However almost all of the newer PICs have an Internal RC Oscillator that can be selected, which will be mentioned in the datasheet.

I would really consider getting hold of a newer PIC, something like a 16F690, or 16F1824/16F1828. These are far more current, and can do anything the 16F84 can do and much more.

If you want to use your 16F84 though, either use an external clock (e.g. from 555 timer or oscillator based on e.g. an inverting gate with RC or crystal) or crystal as specified in the datasheet, or if you don't have an external clock or crystal use the RC option.

First, please return the 16F84 to whatever museum you found it in.

Most modern PICs have a internal R-C oscillator. In fact some, like the 10F series, can run no other way. PICs with enough pins contain a crystal driver. You add the crystal and it's load caps, and the PIC does the rest.

Your PIC is a ancient relic that does not have a oscillator built in. The section (from the datasheet?) you quoted above is a bit misleading. It does have driver circuitry for external crystal or R-C oscillator built in, but not the whole oscillator itself. Note that it also says it cannot operate without external components.

So to answer the question about what you need to make this PIC run, is a crystal and two load caps. You can also find ceramic resonators with the appropriate caps built in, but I'd stick to the crystal.

PIC16F84 is an obsolete microcontroller and it doesn't have internal oscillator.

I suggest you use PIC16F627/628/648 or PIC16F1826/1827. They are compatible and have internal oscillator and much more peripherals.