Another aspect, which isn't mentioned but makes sense (to me, anyway) is level of education. The game assumes most characters can read and write, and presumably do basic maths. It seems a safe assumption that high int characters, typically wizards, spend a lot of time studying. So your low int character probably missed or avoided basic schooling and such, and can just about read but avoids it when possible.
So, for example, if you meet a new type of monster, make your penalized knowledge skill to decide whether or not you know anything about it.
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Smart or dumb, people tend to focus on the things that they feel good at, and shy away from things that they don't feel confident in their ability to accomplish or excel in. This can lead to overcompensation, such as a person who lacks fluency in a local language, or has difficulty reading, showing off their intelligence in other areas, to try and make up for any perception that they are dumb because of their linguisitic / literacy issues.
An Int 7 strong dude with an axe who is hell on wheels when it comes to chopping stuff to bits would likely attempt to find a solution for any dilemna that involves his strength, his axe, excessive force, or, ideally, all three in combination.
There will be times when he will seem almost childlishly pleased with an opportunity to solve a problem with his axe, and even perhaps a bit smug and self-assured afterwards, reminding others of his valuable contribution.
When confronted with several setbacks or disappointments, such as multiple encounters or scenes in sequence where a powerful axe-blow isn't useful, he might get a bit sulky or petulant, and even refuse to cooperate if he thinks that one of his companions is talking down to him by making up some situation where his strength might be useful (or is exploiting his strength by asking him to carry stuff, like a pack mule).
This is just one option, obviously, but I'm thinking of him being kind of like Gollum, from Lord of the Rings, absurdly pleased with himself, and even a bit smug about his contributions, when 'master' is happy with his leading them to Mordor, and sulky and difficult when Sam is belittling his contributions.