OOAD is a methodology

RUP is process

To make it clear.... Process tells what to do. Methodology tells how to approach it.Language tells how to do it

UML is the Unified Modelling Language. This is an amalgamation of work carried out by Booch, Jakobson and Rumbaugh. It details a number of tools for modelling object oriented systems and is a form of Object Oriented Design (OOD).
The Rational Unified Process (RUP) is a development process. that is to say it details the steps involved in designing and developing an object oriented system i.e. what should be created and when. This process is the creation of Rational Corporation (Booch, Rumbaugh and Jakobsen) and builds on their UML.
OOAD stands for object oriented analysis and design (seperately OOA and OOD). This is an area of computer science of which UML forms a part. In simple terms, analysis deals with 'what is required' and design with 'how it shall be provided'. There's also object oriented programming (OOP) which deals with how the solution will be implemented. 
Hope that this is of some use.

UML = Unified Modelling Language. This is a language (not a computer language or a spoken language) that uses pictures to describe pretty much anything. It is often used to describe software systems and business processes.

OOAD = Object Oriented Analysis and Design. This is the way people think and plan when designing software systems using Object Oriented technologies.

RUP = Rational Unified Process. This is Rational Software Corporation's process for designing software and planning business activities.

Process = Just a word. It can be used in lots of contexts, including "Rational Unified Process", processed-cheese, and food-processor. In the software context, it means "the way you plan something".

-chris