How come Deaf people sound weird or speak or type in broken English?
Deaf people who had hearing loss before or around learning to speak have had to rely on visual and tactile methods of learning speech and have had to go through speech therapy. While the vocal cords of deaf people are perfectly intact, it's much harder to speak correctly without a feedback system. It's much like when you hear someone singing to their iPod and they're singing totally out of key and sound crazy, even if they can sing well (or relatively well) when they hear themselves.
With deaf people who have never heard their own voice or the voice of others, it's much harder to self-monitor speech. It's also impossible for someone who is born deaf to know what some or all sounds sound like (depending on the extent of their hearing loss.) So for example, if someone has never heard an "s" sound, it's hard to emulate it.
Some deaf people speak in broken English cause English is not their first language. For deaf people who have grown up with American Sign Language, or whatever other local sign language, English is their second language. So much like a foreigner, they tend to apply the grammar of their own language to English. Just as a foreign speaker might create phrases like "I go to store" or "She do it at her own," someone whose first language is a signed language is speaking English as a foreign speaker as well.
Contrary to popular belief, American Sign Language (and other sign languages in English speaking countries like British Sign Language, Australian Sign Language, or New Zealand Sign Language) have their own rules for grammar and syntax. They have their own ways of forming sentences properly and ordering words and conjugating verbs and so on. They are not just visual representations of the spoken language. This is made evident by the fact that even though the U.S., the U.K. Australia, and New Zealand all have English as a spoken language, they have their own sign languages. So if a deaf person speaks in broken English, think of it as the same as a foreign speaker.
If you are thinking "but this person has grown up in an English-speaking country" or "but this person can read English," it's important to understand that even so, a pre-lingual deaf person hasn't had the same accidental exposure to spoken language as hearing people do growing up. So they have never overheard conversations and had the opportunity to correct their mistakes from exposure.
The only exposure a deaf person has to spoken language is intentional exposure, such as speech therapy or being in a school that advocates speech only. Not only that, but children are taught to read much later than they are taught to speak, so if a deaf person has not had access to signed language, their first access to language is much later than a hearing person's, which can affect the brain's ability to grasp language.
Even though deaf people and hard of hearing people have full access to written language, someone born deaf/hard of hearing doesn't have the same sound associations to letters on the page that someone with hearing does. So they might know the words in written form, but they aren't sounding them out in their heads when reading the way a hearing person is. As a result, even people with hearing loss who have exposure to written language often still miss out on details that are only audible.
If you listen closely, you'll notice the most common mistakes relate to minor changes in sounds (like word endings), such as saying "I wants" (where it's easy to see how a deaf person might miss out on the "s" at the end of "wants") or "I am heated it" (where it's easy to see how someone who hasn't had a lifetime of exposure of when to use "heated" vs. "heating" might mix up the two usages.)
It's important to remember that even if a deaf person has a strange sounding voice or doesn't speak fluent English, it doesn't mean that they're any less intelligent than a hearing person. It's simply a matter of not having the same exposure to spoken language that a hearing person has had. When deaf people are taught visual language, they have no trouble grasping a language.
It's also important to remember that even though some deaf people have a "deaf voice" or speak in broken English, other deaf people master speech and language quite well, so it's impossible to tell the full extent of someone's hearing loss based on their speech and language skills.