There are 3 horizontal motions that make up the winds within a tornado. These three motions are the tornadoes forward motion, The parent tornado circulation, and vortices within the parent tornado circulation. These three motions together make the wind speeds within a tornado extremely variable. Let's look at each in detail. The quicker a tornado moves, the faster the winds will be on one side of the tornado and the slower they will be on the other side. This same phenomena occurs with hurricanes, on one side of the storm the hurricane's forward motion is added to the hurricane's parent wind speed and on the other side the forward motion is subtracted from the hurricane's parent wind speed. (Analogy, if I am running at you and throw a baseball to you, all else being equal, that baseball will get to you quicker than if I was running away from you and threw the baseball to you). The forward motion of a tornado is highly variable (anywhere from nearly stationary to over 70 miles per hour).
The second motion within a tornado is the primary rotational circulation. This is the primary (usually counterclockwise spinning) vortex which makes the tornadoes circulation. This is the primary circulation which determines the wind speeds within a tornado. This circulation can range from less than 70 knots to over 250 knots. There are several factors that determine this wind speed. Some of these factors include helicity (determined by low level speed and directional wind shear), small scale processes, CAPE, and the maturity of the mesocyclone.
The third wind that makes up a tornado are small-scale vortices. These can be thought of and look like mini-tornadoes within tornadoes. They are caused by turbulent friction with the earth's surface along with the hydrodynamic low within a tornado and are most noticeable in strong tornadoes. Relative to a surface observer, the winds on one side of these mini-vortices will be much stronger than on the other side. This is because on one side the tornadoes primary rotational motion is being added to the motion with the mini-vortex and on the other side the tornadoes primary rotational motion partially or completely cancels the motion within the mini-vortex. You can use the same baseball throwing analogy that was given before.
WHAT ARE THE CONSEQUENCES of all these constructive (adding of winds together) and destructive (subtracting of winds from each other) wind motions? The result is extremely variable and chaotic wind motions within a tornado, especially near the earth's surface due to friction. These wind motions are changing constantly (mini-vortices may only exist for a few seconds, then new ones develop and dissipate). This is thought to be one of the reasons why one house can be completely obliterated while a house 100 feet away only has minor damage. Perhaps the house which got obliterated suffered from constructive wind (forward motion side of tornado, addition of winds with a mini-vortex with the tornadoes primary rotational circulation) or perhaps the gradient of wind near a tornado is extremely large, or a combination of both. All these competing and constructive wind motions cause a high variability of wind at the surface in a tornado which can lead to phenomenal and strange damage patterns and stories of extreme damage next to little damage. I must say a lot of what has been stated in this essay is still under research, but this does give you a good working model for wind motions associated with a tornado.