I have seen phrases like the following:
- Till now
- Yet
- Up till now
- As of now
Is there any difference between their usage and meaning, or do they have the same meaning?
Till has the same meaning until has; it is just informal, and not used at the beginning of a sentence.
"Till now" and "up until now" have the same meaning.
Yet is used in negatives, and in those cases you could get it to mean that something didn't happen "up until now." Yet also mean "from now until a period of time mentioned."
They won't arrive for at least two hours yet.
I have never heard as off now being used. It could be "as of now" but I would understand that as "with regards to now." I heard "as of" used in sentences similar to "As of you, you would better be quick." and I am not sure "as of now" would be used with that meaning.
Oxford Dictionaries says that "as of" is used to indicate the time or date from which something starts.
As from 1 January, a free market will be created.
I'm on the dole as of now.
I'm going to talk about "Yet" last, because it is by far the most extensive part.
Till now
It's important to realize that this is actually a misspelling. The correct phrase is 'til now. " 'Til " (quotes spaced out so you can see the apostrophe easily) is a contraction for "until."
Up until now
This is synonymous to 'til now. The "up" doesn't really mean anything and is an artifact of colloquialism.
As of now
This phrase means "starting from now." You can think of it as the opposite of "'til now;" whereas "'til now" describes the past, leading up to the present, "as of now" describes the time immediately after the present and leading into the distant future. "From now on" is another set phrase that means the same thing. Here is an example:
As of now, we will no longer be serving breakfast in the cafeteria.
Yet
This is a much more versatile word in the English language than to be simply used for indicating a period of time. "Yet" can be used as a conjunction when the joined sentence expresses a contrasting thought, in the same way that "but" can.
I've got everything a working man could ask for, yet I feel like something is missing from my life.
It can also be used as an adverb that indicates the action a verb describes hasn't been performed.
We apologize for the delay, but our support team has yet to resolve this issue.
This construction is always "has yet to [verb]," where [verb] is the action the subject hasn't done yet. You can also use "yet" at the end of a sentence, like I just did in the last one. In this context, there is always a helping verb ("hasn't") in the phrase for the main verb ("done") which the subject hasn't performed.
To build off of kiamlaluno's answer, you can use future tense with "yet" to indicate how long it will take for something to happen. A present-tense version of the sentence kiamlaluno used using the construction I just mentioned would look like:
They haven't arrived yet.
In contexts where more formal language is required, you can also use this construction:
They have not yet arrived.
It's similar, except "yet" is always put right before the verb. Always avoid contractions in formal context.
"Yet" is a word with a myriad of uses. In the interest of brevity, I encourage you to find grammar articles about this word specifically if you wish to know its full details of usage. You can probably find a good question and answer about it on the English Language & Usage SE.