Isogametes and oogametes
Allow me to start off with a nice picture showing the differences - note female gametes are on the left while male gametes are on the right in my examples:



Isogametes 

For a gamete to be considered an isogamete the other gamete that it meets up with to produce is exactly the same in both size, structure and movement. [2] It is literally trying to find itself. The "male" and "female" are literally no different and it is impossible to tell which is which. 

When you look at the picture the two gametes are exactly the same in every way except that they are facing each other in this picture. 



The next two are forms of anisogamy:

(source: ulsfmovie.org)  

Heterogametes 

These gametes differ in at least one of the following:


size
structure
sex


Although it can also be a combination of these three things. [3] As you can see here the female can be structurally the same as the male. (Bottom and top examples of the second picture). From my understanding (although someone can come and prove me wrong) Oogametes are a specific from of heterogamous.

Oogametes 

Oogametes differ in size, sex AND function. Females are stationary while males move. [4] Females are also much larger than males. (For instance in humans the cell that divides to make sperm divides equally while the cell that divides in the female divides to make one egg and three polar bodies.)