RC oscillator model in attiny microcontroller
As far as I know all Atmel microcontrollers I've encountered do have an internal oscillator. It cannot be separated from the chip as it's manufactured with an RC oscillator embedded in the chip. However you can just not-use it as soon as you stick a crystal oscillator to the unit. Note that it might be impossible in low-pin number units.

From my experience the RC oscillator is rather unstable as I measured its frequency to drift by quite a non-negligible amount. The drift increases with temperature. If you don't need time accuracy it's good enough. But if timing accuracy is critical, like in serial communications such as high-speed RS232 or CAN, an external (crystal) oscillator is recommended.

As you read in the data sheet, the frequency of the internal oscillator can be adjusted in steps. This is achieved indeed through the OSCCAL register. You may be limited by the internal PLL though (which the internal oscillator also feeds, depending on how you set the fuses) so the frequency adjustment that can be made is also limited. Refer to the data sheet for the exact limitations.

As Chris Stratton explained the oscillator frequency is trimmed in an analogue way.