How to call JavaScript function instead of href in HTML

If you only have as "click event handler", use a <button> instead. A link has a specific semantic meaning.

E.g.:

<button onclick="ShowOld(2367,146986,2)">
    <img title="next page" alt="next page" src="/themes/me/img/arrn.png">
</button>

That syntax should work OK, but you can try this alternative.

<a href="javascript:void(0);" onclick="ShowOld(2367,146986,2);">

<a href="javascript:ShowOld(2367, 146986, 2);">

UPDATED ANSWER FOR STRING VALUES

If you are passing strings, use single quotes for your function's parameters

<a href="javascript:ShowOld('foo', 146986, 'bar');">

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