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Your plant is becoming "leggy" because it is in a low light environment. Increasing the amount of light it receives, by adding another grow light or moving it to a sunnier window, is the best way to fix the problem. Also see this article:

https://www.gardeningknowhow.com/plant-problems/environmental/established-plants-leggy.htm

The flowers don't have the same flavor or scent intensity. This article may help
https://www.gardeningknowhow.com/edible/herbs/oregano/drying-oregano.htm

You can still use it, but often when something bolts like that, it will make the flavor, either over bearing or bitter.

Here is an article for more information:https://www.gardeningknowhow.com/edible/herbs/hgen/cutting-off-the-flowering-tops-on-herbs.htm

It is likely that the plant's roots were harmed beyond repair. It is best to make sure the ground is, thoroughly, wet before digging. This will help to ensure that the roots are not damaged.

Here is an article for more information on the care of this: https://www.gardeningknowhow.com/edible/herbs/oregano/learn-how-to-grow-oregano.htm

The plants you mentioned like hot, dry conditions so overwatering is more likely to kill them than under-watering. Both have about the same effect on the plant, leaves shrivel and die. If these plants are in clay soil, the soil must be amended to let it drain faster. (They must dry out between waterings or the roots will rot.) Adding perlite, sand or pea gravel is a must down at least 8 inches. If grown in containers, make sure they have drainage holes in the bottom and add sand or perlite to the potting mix so it is about 1/4 sand/perlite. Do not use fine grain sand like play sand. Look for coarse "builders' sand". If my hunch doesn't seem right, please repost with a picture and tell us how you are caring for your herbs.

You have many options here. The safest way to do this without making the soil toxic would be to pour boiling water on everything in there once per day until it is all dead. This will not take long, and can happen with the first application.

I always recommend planting invasive herbs in container. This will ensure that the plant cannot spread. It can be difficult to control once they get established.