Is there any sect of Judaism that interprets both the written Torah and oral Torah literally?
Your question presents contradictory ideas.
Anyone that accepts the validity of the Oral law has inherently acknowledged that he is not translating the Written Law literally. That's the whole reason for having the Oral Law.
As an example - The Torah says, "An eye for an eye". Literally, that means if I take out your eye, you take out mine (assuming you can see well.) But, if you accept the Oral Law's validity, you accept that it has not taken the Written law literally, for the Oral Law explains that it means that the damager compensates you monetarily.
You can't interpret the oral torah literally because, by its nature, it is not definite. At the "end user" side of the oral law, there is a Rabbi who will give a ruling, but there could have been a different rabbi who would give a ruling.
If your Rabbi gives you a ruling, unless he is talking cryptic and yoda-like, that is the law and you have to take it literally.
If he uses a figure of speech and you decide to interpret that literally and subvert the ruling, then that should not be interpreted literally.