Should I consider buying or move on?

I like the 2007 Honda Odyssey ex-l. I test drove one recently that's at a good price and miles. The only problem is that the steering wheel shakes above 50mph and continues while at 70 to 75mph. Should this be an automatic deal breaker or should I consider buying and bring to mechanic to inspect? I hate to waste money for multiple mechanic inspections.

Don't go with this vehicle when you have too many other options.

If you know nothing about cars and don't know how to decide if a purchase is a good idea you should take the car to a mechanic BEFORE you buy it so you get an idea of how much money you'll need to spend on maintenance it needs.
The vibration may just be tires out of balance.

If the car is at a dealership tell them that is the reason you don't want to buy it. If they can get the problem fixed then you will talk.
That also might be what to do if it is a private seller.
There's no reason for you to invest in having some one look at problem if you can get it fixed with out paying for it.

Do not purchase without getting the frontend looked at by one or more front end shops. Could be a couple of hundred dollars or something not fixable at all.

Move on. There are THOUSANDS of used cars for sale without major issues.

Seems like it needs wheel balancing. Not a biggie, but suggest to the seller he pays for it

Most common problem is the tires are not dynamically balanced. At slow speeds you do not notice it but at high speeds you do. I would ask the seller to balance the tires and if that does not fix the problem, go to a different car.

The front tires are not balanced. That is all that is. Mechanic can't fix it. Take it to a tire store and have them check for wheel balancing. You got the shakes. They know what to do.
At most the only other mechanic you would see would be a Wheel Alignment shop and they check out the front end when you mention the shakes(that is if the balanced tires did not fix it). The wheel alignment shops know of all the parts under the car by memory. This is ALL they ever see.
You are getting a USED VEHICLE. Not everything is going to be PERFECT CONDITION FOR A CAR THAT IS 11 YEARS OLD. You got to EXPECT SOMETHING TO BE WORN(hoping for nothing but also being realistic)

If it is such a good deal, someone else will buy it because they KNOW THAT IS THE PROBLEM. They win, you lose.

Tell the seller to balance the wheels first, then try the car again.