My family needs to send me approximately $3000-5000 for my expenses here in Michigan and they found a relative coming to US in coming days. They would give him cash in my country and he would carry it to US. Once he is here, he will transfer the money from his bank account to mine. Is it illegal for me to receive the money this way?
Normally it is completely legal for your family to send you money from their country directly to you in the US. (Are you in a country that doesn't have a banking relationship with the US?) They can do this in a variety of ways, all of which probably have a nominal fee. It sounds like instead of doing that, the plan is for your family to give $3-5k in cash to a relative, ask them to bring it to the US, deposit it into a US bank account, and then transfer the money to your account. IMHO it's not worth the hassle (and risk of it getting lost or stolen) just to avoid the nominal fee.
But to answer your question, it is also completely legal for your relative to enter the US with any amount of cash. If the amount of cash is more than $10K, then it should be declared (and this is not a big deal- it's just a simple form), and in this case since it's less, it doesn't need to be declared. Once in the US it's also legal for your relative to deposit the money into their account and transfer it to yours. But again, this is a lot of extra work which is "strange" compared to just sending it in the first place. If anything, doing this runaround is more likely to raise questions than simply wiring the money in the first place.
As for your title question, my understanding is that this is probably not considered hawala simply because it's flowing through a bank. (Though I'm curious why you ask- does it matter to you if this is considered hawala?)
There is no law that prevents you from receiving money from your family, unless the money is somehow associated with an illegal activity. However cash transaction over $10000 need to be reported.
Cash transactions under $10000 do not need to be declared or reported to the IRS.
Make sure that your relative does NOT carry a total of $10000 or more in cash (or cash equivalent), when they enter to the US. This would need to be declared and this can be rather unpleasant and lengthy discussion .
The hawala system does not involve banks at all, and it does not involve any transportation of currency across political boundaries. The way it works is that if you want to send money from City A to a payee in City B (which may, or may not, be a different country), you give cash money X in currency C to your friendly neighborhood hawala broker in City A who then calls his pal hawala broker in City B to deliver cash money Y (perhaps in currency D if A and B are in different countries) to your payee. So, how much should you pay your hawala broker? He will tell you: it will cost X in currency C to deliver Y in currency D to your payee. The advantages in a cash society is that there is no paper trail at all and so no need to bother with taxation at either end, or currency import/export regulations etc. It is all done by phone. How can it work? Well, hawala currency transaction occur in both directions, and the hawala brokers keep track of how much they owe each other.
That being said, the OP's transaction is not a hawala transaction at all since the money, whether it is converted from currency C to US dollars (currency D) in City A itself, or transported as currency C into the US and then deposited in a US bank (and the best of luck to Uncle Jack as he tries to deposit foreign currency into a US bank). All that is being avoided is currency export regulations if City A is located in a country from which it is not easy to send remittances in US dollars to the US, or if it is illegal to possess US dollars and so the currency conversion to US dollars in City A is being done on the black market.
First, this is NOT how Hawala works. Hawala merchants don't carry cash around as an easy target by robbers.
Second, your family should use P2P money transfer port which imitates the Hawala to your bank account. Because those portals are recording the transaction and abided to destination country jurisdiction, thus save everyone the hassle.
I want to refute @Dilip Sarwate point of Hawala. Peer-to-Peer(P2P) Money transfer portal that uses a local bank account as a proxy to disperse fund is still Hawala. In P2P money transfer, money is neither physically carried around, nor using any money exchange facilities. Most P2P money transfer portal only works by credit the recipient bank account is to eliminate the need for a costly service counter or third party agent, thus reduce the cost and also risk when scrutinize by various country anti-money laundering law.
In addition, the part of anonymity is only half-true. In many countries, money-exchanger that use Hawala must also abide by local country anti-monetary laundering law. They must report to the authority if the transferred amount hits the threshold, otherwise, they will risk their license being revoked by the authority. Nevertheless, there are loopholes(breaking it to many smaller amount), or make use of unlicensed money traders that will perform the anonymous Hawala, in which, the client has to bear the high cost and the risk themselves.
The main reason that Peer-to-Peer money exchange tries to distance themselves from Hawala is mainly marketing. Afterall, Hawala is demonised with propaganda machinery as money laundering tools.