I have to write my answer in English. I hope you won't get confused.
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他带着奇怪的眼神看着我。
Tā dàizhe qíguài de yǎnshén kànzhe wǒ.
He looked at me strangely.
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I think the reason why 带着奇怪的眼神 was translated into a simple word "strangely" is that there is no good English translation for the Chinese word 眼神 that means the "expression in one's eyes". (Your eyes will look different when you laugh and cry, just like facial expression, we name it as 眼神.) If I were the translator, I would translate the sentence into "He's looking at me with a strange expression in his eyes." And "expression in one's eyes"(眼神) is intangible, the translator just left them out.
Let's look at the second sentence "She spoke with a thick American accent." In this sentence, "with" means "带着", "a thick American accent" means "浓重的美国口音". Obviously, "accent" is intangible.