How to copy a text file odd lines and another file even lines and dump it in another

To work more easily with even and odd lines, I propose you to dump the contents of the files to each ArrayList<String> and work with them.

Dump the content of BufferedWriter to ArrayList<String>

This can be done in several ways. From Java-8 , it's almost trivial:

// Java 8
try (BufferedReader brPar = new BufferedReader(new FileReader("origen.txt"))) {
    List<String> pares = brPar.lines().collect(Collectors.toList());
}

With Java-7 , it's a bit more complicated:

// Java 7
try (BufferedReader brImpar = new BufferedReader(new FileReader("origen2.txt")))
{
    String line;
    impares = new ArrayList<>();
    while ((line = brImpar.readLine()) != null) {
        impares.add(line);
    }
}

Maybe you can separate it in another method like this:

private List<String> volcarALista(BufferedReader reader) throws IOException
{
    String line;
    List<String> lista = new ArrayList<>();
    while ((line = reader.readLine()) != null) {
        lista.add(line);
    }
    return lista;
}

// Java 7
try (BufferedReader brImpar = new BufferedReader(new FileReader("origen2.txt")))
{
    impares = volcarALista(brImpar);
}

Work with your ArrayList<String>

When you have filled them, working with your lists requires a simple % for :

try (BufferedWriter bw = new BufferedWriter(new FileWriter("destino.txt"))) {
    for (int i = 0; i < pares.size(); i++) {
        bw.write(impares.get(i));
        bw.newLine();
        bw.write(pares.get(i));
        bw.newLine();
    }
}

Although you think if your files do not have the same number of lines, this could lead to errors . You could solve it by checking which list is bigger.