Is the phrase " Black market " correct? Meaning illegal or undeclared work and are there any other words or phrases, that are used to describe this kind of work or jobs?
"Black market" is a broad term, usually meaning trade of illicit goods or bypassing legal channels in trade of restricted goods.
The terms you're looking for are Unreported employment, "working under the table", being paid cash-in-hand or moonlighting, a domain of Grey economy - activities that could be legal if passed through legal channels, but due to, e.g. tax evasion, constitute illegal activity.
The black market is as its name suggests, a market; somewhere specific goods or services are exchanged outside the eyes of the law.
The black economy or underground economy is broader, and includes cash-in-hand and other undeclared income sources, which is more in line with what you mean I think.
definition: The part of a country's economic activity which is unrecorded and untaxed by its government.
Black market indicates the trades of goods (sometimes services) in a non-regulated market outside the view of legal and legislating instances, which means that not only are (some) taxes unlikely to be paid, but other legal details may be overlooked as well (consumer protection, anti-trust legislation, warranty, etc.)
This kind of market operates usually illegally, but not all illegal work or work that is not declared for the taxes would be considered as part of a black market, or a black market in their own right.
Note that not declaring proceeds from work for tax purposes can be illegal, but that does not mean the work itself has to be illegal:
If I sell drugs, in many countries that is illegal work.
If I paint your house and I do not declare my revenue, the work was not illegal.