This is a prime candidate for the [Strategy pattern][1].

For example, this code:

    if ($this->isDisputeAccepted($order)) { //returns true if dispute was accepted
        $order->setStatus('accepted');
        $order->refund(); //refunds the order on ebay and internally in my system
        $this->insertRecordInOrderHistoryTable($order,'refunded');                        
    } else if ($this->isDisputeCancelled($order)) { //returns true if dispute was cancelled
        $order->setStatus('cancelled');
        $this->insertRecordInOrderHistory($order,'cancelled');
        $order->rollBackRefund(); //cancels the refund on ebay and internally in my system
    } else if ($this->isDisputeOlderThan7Days($order)) { //returns true if 7 days elapsed since the dispute was opened
        $order->closeDispute(); //closes the dispute on ebay
        $this->insertRecordInOrderHistoryTable($order,'refunded');
        $order->refund(); //refunds the order on ebay and internally in my system
    }

Could be reduced to

    var $strategy = $this.getOrderStrategy($order);
    $strategy->preProcess();
    $strategy->updateOrderHistory($this);
    $strategy->postProcess();

where getOrderStrategy wraps the order in a DisputeAcceptedStrategy, DisputeCancelledStrategy, DisputeOlderThan7DaysStrategy, etc. each of which know how to handle the given situation

  [1]: http://www.labelmedia.co.uk/blog/posts/design-patterns-strategy-pattern.html