Like google is a verb, is java a word? Can I say "I java"?
I am wondering if it works that way, or if I have to say, "I do java."
What you're talking about is colloquially called the "verbification" or just "verbing" of nouns that do not have any standard verb forms. This is a fairly common way to play with English language norms:
Abel: You say you cook? Like what?
Blain: Well, I salad, I soup, and sometimes I spaghetti.
With the understanding that it is a colloquial and informal usage, and therefore kind of humorous: yes, you can say:
Otherwise, in a more formal situation, say:
I can do Java. / I can program in Java.
(Edit) As with many clever and colloquial expressions that play with normal language patterns, context is key. Saying "I spaghetti" is meaningless without a context that defines whether you mean you eat it, cook it, tangle things up like it, or some other possible definition. For example:
I tried to fix the legacy code, but I'm afraid I just spaghetti'd it up even more.
This is a play on the programming expression "spaghetti code". If you are aware of this expression, the meaning of "spaghetti'd" is obvious. If you are not aware of it, then the meaning will be confusing. In the same way, "I Java" would not have the intended meaning (and humor) outside of an informal conversation about programming languages.
As with any colloquial usage, the question of can you say something is separate from the question of whether you should say something. It depends on how familiar you are with the nuance. Do you know exactly what the expression means? Are you aware of its origin? Have you considered any alternate interpretations that might be misleading or even offensive? Would your audience appreciate your cleverness, or would they think less of you for it? And many others.
That's really a question for meta, as it's less about learning English as it is about learning any language. For now, I'll leave this answer as is, and expect that English learners will understand my caveats to the explanation.
I don't know of a context in which "Java" wouldn't be a proper noun or adjective, except perhaps as a (rare?) colloquialism for coffee. If you're worrying about correctness, you should certainly capitalize it.
It would sound pretty strange to people if you used it as a verb. I think part of this is that "Java" has other meanings besides the programing language. Specifically, it's a large island in the Pacific, and coffee from Java is sometimes called "java".
In theory, you can verb any you like, but even if everyone understands you (and they may not), they'll still think you sound wrong.
No, "I Java" does not work in the same way.
'To google something' has become synonymous with 'to use a search engine to search for something', partly because of Google's dominance in the market and partly because there was no concise way to express that same idea unambiguously; it evolved out of convenience. When this happens, the trademark is said to have become genericized. It's fairly rare but by no means exclusive to Google.
Other examples include "that looks photoshopped", (in the UK) "I hoovered [vacuumed] the carpet", "the police tasered the suspect".
There really isn't an easy way to know whether a company or product name can be used as a verb. Usually you can't. It's simply a matter of experience to learn the exceptions.
In your case I would say "I program/code in Java".
If you're talking about Java (the language) I'd say:
"I write Java" or "I program in Java" rather than "I do Java". You could say: "I can do Java" but it does not necessarily mean you are doing so currently, it just means you have the ability to write Java.
As a programmer, I'd say you "use" Java, or you "code in" Java. You can say you're a Java programmer, if that's your primary language, but it'd be very nonstandard (though probably still understandable by programmers) to say that you Java.
While using many nouns as verbs is perfectly valid in the English language, verbifying a noun is also a subtle art that requires a fair amount of cultural context to do right.
In the specific example, using the name brands Google and Java, one is often used as a verb that is synonymous with doing an online search, because it is the most common way to search online, by far. Java, though, is one semi-popular programming language out of many. While a native speaker might be able to figure out your meaning through context, if someone were to tell me "Let's java it up," I would be more likely to think that they're asking me to accompany them to a cafe than to think that they want us to go write some software using the Java programming language.
For most nouns, though, the verb form only imparts a specific quality of that noun, and not every quality.
For example, when using "floor" as a noun, it means to bring something low, rather than to make something a surface for walking. For instance, in signal processing, to floor a signal means to completely suppress it. In math, to floor a number means to round it down, even if normal rounding techniques would round it up. (17 becomes 10.)
A doughnut (also spelled donut; both spellings are correct, with "donut" becoming more common) is known for being a small circle. "Doing doughnuts" while driving means to drive in very tight circles, especially so that you lose traction and leave circular skid marks on the road. "To doughnut" has nothing to do with pastries, carbohydrates, frying, etc.
To plank is to hold your body rigid, often over a gap or against a wall, pretending to be a wooden board.
There can also be unexpected meanings of a verbified noun. When in a car, "flooring it" means to go very fast, rather than lowering the car. (The subject of the phrase "floor it" is referring to the accelerator pedal, rather than the car... To floor that pedal is to push it as close to the floorboard as possible.)
Additionally, to groove is specific to some regions of North America, and is losing usage. It is roughly synonymous to dancing, and comes from the grooves on pressed vinyl records.
Most native English speakers will not attempt to create new verbified nouns unless they are in an extremely informal setting and are attempting to be humorous. We also do not expect nouns to be verbified in general, except for the ones that we already think of as verbs through common use, such as to google, to do doughnuts, to floor it, etc. If someone already speaks English fluently, we can figure out their meaning with a moment of thinking, but if someone isn't fluent, we'll assume that they misunderstand the rules of the language, and often won't be able to infer the intended meaning.
And back to the original phrase in question, "I java..." There is already a verbified noun that means what you intend to say: Program.
A program is a list of instructions to accomplish a task. It was verbified in the 1970's to include writing software. "I write programs in Java" can be shortened to "I program in Java," but it would lose too much meaning to shorten it further to just "I Java." It would be like trying to say "I draw with yellow paint," but shortening it too far to just "I yellow" instead of "I paint in yellow." And just as Java is both a programming language and a type of coffee, yellow is both a color and a slang term for cowardice. If I heard someone say "I yellow," I would assume they're admitting to being afraid, just as I'd assume that someone who wants to java would want to drink coffee.
In any case, I would not say that "I do Java" unless the conversation were already firmly established in the context of writing software. For example, "Which programming language do you use?" "I do Java, PHP, and C++."