The 13th Amendment was very effective. The other two were not very effective at all, at least not for about 90 years after they were ratified.
The 13th Amendment abolished slavery. Since there was little opposition to this and since it was easy to enforce, it was very effective. Slavery was effectively ended by the Civil War and by that amendment.
The 14th Amendment gave blacks equal rights and the 15th guaranteed them the right to vote. These amendments were hardly adhered to in any way. "Jim Crow" laws circumvented the 14th Amendment while things like literacy tests, poll taxes, and the "white primary" prevented blacks from voting. It was not until the Civil Rights Movement that these amendments became effective in any real way.
Primarily, The Thirteenth Amendment, 1865 abolished slavery and involuntary servitude. It completed the task of the Emancipation Proclamation. The Fourteenth Amendment, 1868 made the former slaves citizens. It provided for equal protection of the laws for all citizens. The Fifteenth Amendment, 1870 provided the right to vote for Black males. This itself brought political and economic equality to the former slaves. But the point is even though slavery was abolished, the treatment, the attitude towards them, African Americans didn’t change.
South formed the Black codes. Under these codes blacks didn’t not have the right to bear arms, be involved in any jobs other than farming. The south was a society where they couldn’t live without slaves. Slaves were a major labor source. For it to be take out, it would cause chaos. This is what exactly happened. The effectiveness of these constitutional amendments were hindered by these unnecessary rules imposed by the south. These often slowed down reconstruction. In addition, the KKK were groups that opposed Black having the right to vote. The weakness and hindrance is shown in the Supreme Court case United States v. Reese. It was a case in 1876 in which the Supreme Court upheld practices as the poll tax, the literacy test, and the Grandfather Clause. This case definitely helped undermine African American and their rights stated in the 15th Amendment. Sharecropper was another factor that was evolved from Reconstruction that put many African Americans in debt!
On the other hand, many rights and acts were passed to support the constitutional amendments. Freedmen’s Bureau, which was established in March of 1865 to care for refugees. Carpetbaggers went to the South to oppose the practice of slavery and they went to check on how the black were being treated. Civil Rights act of 1866 declared black as citizens of the United States, this strengthened the 13th Amendment.