It may be that the Invoice description being sent is to long, that field has a maximum length of 255 characters. try changing line 628 - 629:
$eWAY_XML_itemized[0][1] = "ewayCustomerInvoiceDescription";
$eWAY_XML_itemized[1][1] = "".$WA_Store_Cart->TotalColumn("FullDetails") ."";
to use a hard coded value like:
$eWAY_XML_itemized[0][1] = "ewayCustomerInvoiceDescription";
$eWAY_XML_itemized[1][1] = "My Store Order";
for the email to be able to send, line 971:
$WA_redirectURL = "checkout_success.php";
must be changed to:
$WA_redirectURL = "";
If that is not working, double check that you are using the correct SMTP server address in the WA_Globals. If the SMTP server is correct, contact the host to see if they can take a look at the SMTP server error logs to see why the email is not being relayed.