Is it ok to use grass clippings collected from near the road on my vegetable garden?
Yep, depending on how you will use them, either in a compost pile or for a mulch - you may see more weed seeds sprout if the grass was high when it was cut, and then you turn it into the soil as an amendment.
Composting should get most of the weed seeds to sprout and die from lack of sunlight under the pile. If you already have a weed control method in place, no worries.
Is there a weed control program in your area? Some local governments spray road right-of-ways to control weeds and they are permitted to use some herbicides that can be a potential problem for your garden.
agree with pt03.
If your road people will be spraying poisons along the roads to control "weeds" and growth of grasses they are required to notify those living near by and those people have an opt out clause. If you do not want your roadside sprayed you can tell them not to.
One year my county road commission was proposing spraying and I asked with what and eventually was provided the mix. When I pointed out to them that the formula was very similar to that of Agent Orange sprayed in Viet Nam the road commission dropped that idea altogether.
Can you use the clippings from the roadside as mulch in a vegetable garden? Sure, but be aware they will be polluted with what is worn off the vehicles, rubber from tires, oil, what is in exhaust, whether that road side is sprayed with poisons or not. I find in the grass in my road side all kinds of trash that I would not want in my gardens including cigarettes and cigars, plastic, syrofoam, paper, car parts, etc.
residuals aside, grass clipping added on top can mat down and stop rain penetration and can germinate seed of the grass and anything else that maybe there. so i would suggest put the clip on the garden around but not up to the plants and cover with other mulch.
Here is a link that might be useful: lens garden page