*NIX (Linux, OS X, ...)

Use n, an extremely simple Node version manager that can be installed via npm.

Say you want Node.js v0.10.x to build Atom.

npm install -g n   # Install n globally
n 0.10.33          # Install and use v0.10.33

Usage:
n                            # Output versions installed
n latest                     # Install or activate the latest node release
n stable                     # Install or activate the latest stable node release
n <version>                  # Install node <version>
n use <version> [args ...]   # Execute node <version> with [args ...]
n bin <version>              # Output bin path for <version>
n rm <version ...>           # Remove the given version(s)
n --latest                   # Output the latest node version available
n --stable                   # Output the latest stable node version available
n ls                         # Output the versions of node available

Windows

Use nvm-windows, it's like nvm but for Windows. Download and run the installer, then:

nvm install v0.10.33         # Install v0.10.33
nvm use v0.10.33             # Use v0.10.33

Usage:
nvm install [version]        # Download and install [version]
nvm uninstall [version]      # Uninstall [version]
nvm use [version]            # Switch to use [version]
nvm list                     # List installed versions

Easiest solution would be to try the following to cleanup your node issues and reinstall a clean version.

First remove everything related to node

sudo apt-get purge --auto-remove nodejs npm

UPDATE For yum:

yum clean all
yum -y remove nodejs

Remove these leftover files and folders as well

sudo rm -rf /usr/local/bin/npm /usr/local/share/man/man1/node* /usr/local/lib/dtrace/node.d ~/.npm ~/.node-gyp /opt/local/bin/node opt/local/include/node /opt/local/lib/node_modules 

Then install node back with nvm,

curl -o- https://raw.githubusercontent.com/creationix/nvm/v0.33.6/install.sh | bash

//To uninstall a node version 
//nvm uninstall <current version>

nvm install 8.8.1

nvm use 8.8.1

//check with 
node -v
npm -v


//**UPDATE**: Install your package
npm install -g n

And all should work.

UPDATE : Install Without NVM

yum install -y gcc-c++ make
curl -sL https://rpm.nodesource.com/setup_8.x | sudo -E bash -

yum install nodejs
node -v

//Install your package
npm install -g n

nvm list

This command worked fine for me. It will list all the installed versions of node under nvm

At https://nodejs.org/dist/ there is index.json which indicates each version of nodejs and which version of npm is bundled with it.

index.json

An excerpt from one of the objects in the array of index.json reads:

[
  {
    "version": "v10.6.0",       //<--- nodejs version
    "date": "2018-07-04",
    "files": [
      ...
    ],
    "npm": "6.1.0",             //<--- npm version
    "v8": "6.7.288.46",
    "uv": "",
    "zlib": "1.2.11",
    "openssl": "1.1.0h",
    "modules": "64",
    "lts": false
  },
  ...
]

Whereby each object in the array has a version (i.e. the nodejs version) and npm (i.e. the npm version) key/value pair.

Programmatically obtaining the versions

In-browser Snippet

(async function logVersionInfo() {
  try {
    const json = await requestVersionInfo();
    const versionInfo = extractVersionInfo(json);
    createVersionTable(versionInfo);
  }
  catch ({ message }) {
    console.error(message);
  }
})();

// Promise-wrapped XHR from @SomeKittens' answer: 
// https://stackoverflow.com/a/30008115
function requestVersionInfo() {
  return new Promise(function(resolve, reject) {
    let xhr = new XMLHttpRequest();
    xhr.open('GET', 'https://nodejs.org/dist/index.json');
    xhr.onload = function() {
      if (this.status >= 200 && this.status < 300) {
        resolve(xhr.response);
      } else {
        reject({
          status: this.status,
          statusText: xhr.statusText
        });
      }
    };
    xhr.onerror = function() {
      reject({
        status: this.status,
        statusText: xhr.statusText
      });
    };
    xhr.send();
  });
}

function extractVersionInfo(json) {
  return JSON.parse(json).map(({ version, npm = '-' }) => 
    ({ nodejs: version.replace(/^v/, ''), npm })
  );
}

function createVersionTable(array) {
  const table = document.createElement("table");
  table.border = 1;

  const headerRow = document.createElement('tr');

  for (const headerText of Object.keys(array[0])) {
    const headerCell = document.createElement('th');
    headerCell.textContent = headerText;
    headerRow.appendChild(headerCell);
  }

  table.appendChild(headerRow);

  for (const el of array) {
    const tr = document.createElement("tr");

    for (const value of Object.values(el)) {
      const td = document.createElement("td");
      td.textContent = value;
      tr.appendChild(td);
    }

    table.appendChild(tr);
  }

  document.body.appendChild(table);
}

td { padding: 0 0.4rem; } tr:nth-child(even) td { background-color: antiquewhite; }

Node.js Script

Consider utilizing the following node.js script to request the data from the https://nodejs.org/dist/index.json endpoint.

get-versions.js

const { get } = require('https');

const ENDPOINT = 'https://nodejs.org/dist/index.json';

function requestVersionInfo(url) {
  return new Promise((resolve, reject) => {
    get(url, response => {
      let data = '';
      response.on('data', chunk => data += chunk);
      response.on('end', () => resolve(data));
    }).on('error', error => reject(new Error(error)));
  });
}

function extractVersionInfo(json) {
  return JSON.parse(json).map(({ version, npm = null }) => {
    return {
      nodejs: version.replace(/^v/, ''),
      npm
    };
  });
}

(async function logVersionInfo() {
  try {
    const json = await requestVersionInfo(ENDPOINT);
    const versionInfo = extractVersionInfo(json);
    console.log(JSON.stringify(versionInfo, null, 2));

  } catch ({ message }) {
    console.error(message);
  }
})();

Running the following command:

node ./path/to/get-versions.js

Will print something like the following to your console:

[
  {
    "nodejs": "14.2.0",
    "npm": "6.14.4"
  },
  {
    "nodejs": "14.1.0",
    "npm": "6.14.4"
  },
  {
    "nodejs": "14.0.0",
    "npm": "6.14.4"
  },
  {
    "nodejs": "13.14.0",
    "npm": "6.14.4"
  },
  ...
]

It lists each version of Node.js and its respective NPM version.