it appears that you are category "D" which appears to be taxed by the state at 15%. There may be exclusions...Please contact either a tax advisor.
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Lets assume that this is subject to state inheritance tax. The second part of your question suggests another important point, which is that if this is taxed, you may yet be entitled to have your inheritance taxes paid by the estate-- rather than come out of your specific bequest. Get a copy of the will and read it and consider asking the executor what is planned in this regard. If it sounds bad hire a NJ lawyer who knows about estates to protect your interests.
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Probably -- depends on what the will said and whether the estate is paying your bequest on gross basis or after-tax. If the will does not specifically state that you are receiving your $20K and the estate pays for the inheritance tax then by default your $20K will be reduced by the tax due (remitted by the estate executor to NJ on your behalf) which will be 15% on the amount in excess of $500 .... meaning $2,925 leaving you a net distribution of $17,075. You are a Class D beneficiary as per NJ distinctions made among different classes of beneficiaries.
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It is possible that you will not have to pay the NJ Inheritance Tax. If the will has a tax apportionment clause that says that all estate and inheritance taxes are paid out of the residuary estate, and if the will left each niece and grandniece a specific bequest, then you may be in luck. Depends on the value of the rest of the estate and other factors. My office is in Randolph, NJ if you need assistance.