Diesel, one of the examples in your question, has been an Italian clothing brand for decades. It's also the name of a couple of bands, couple of films, a game engine, a surname and the name of a military operation in 2009.
Tornado, another one of your examples, is a community in West Virginia, the name of many amusement rides, the name of Zorro's horse, the name of multiple films, songs and games, the name of a clothing retailer, a Python webserver, a HTC phone, a couple of sports clubs and multiple military weaponsystems.
According to the United States Patent and Trademark Office (USPTO):
A trademark can be any word, phrase, symbol, design, or a combination of these things that identifies your goods or services. It’s how customers recognize you in the marketplace and distinguish you from your competitors.
You become a trademark owner as soon as you start using your trademark with your goods or services. You establish rights in your trademark by using it, but those rights are limited, and they only apply to the geographic area in which you’re providing your goods or services. If you want stronger, nationwide rights, you’ll need to apply to register your trademark with us.
If you're referring to a Diesel t-shirt, customers will recognize it. If you're referring to a Tornado shop in Japan, customers will recognize it.
Can an everyday word be trademarked? Clearly. Whether that has the actual effect that you think a trademark has, is another question.