Hi Pascal

Due to that is a nested local function there is no way that you could extend that function using any kind of JS inheritance technique, you could only have at least 2 choices here.

1- You could disconnect that js file using Odoo xml extension like: 

<template id="assets_frontend" inherit_id="website.assets_frontend" name="Shop">
    <xpath expr="//script[@src='/website_sale/static/src/js/website_sale.js']" position="remove"/>
    <xpath expr="." position="inside">
        <script type="text/javascript" src="/your_website_sale_module/static/src/js/website_sale.js"></script>
    </xpath>
</template>

And provide yours with the proper changes, that is a valid way to change JS in extreme scenarios in Odoo 

2- Disconnect the events binding functions that use the price_to_str function in order to rebind it with a new version of the event binding using a new local nested version of the price_to_str function, using jquery.off

http://api.jquery.com/off/

Like:s

$(document).ready(function () {
    function update_product_image(event_source, product_id) {
        var $img = $(event_source).closest('tr.js_product, .oe_website_sale').find('span[data-oe-model^="product."][data-oe-type="image"] img:first, img.product_detail_img');
        $img.attr("src", "/website/image/product.product/" + product_id + "/image");
        $img.parent().attr('data-oe-model', 'product.product').attr('data-oe-id', product_id)
            .data('oe-model', 'product.product').data('oe-id', product_id);
    }

    $('.oe_website_sale').each(function () {
        var oe_website_sale = this;
        
        //your new function
        function price_to_str(price) {
            price = Math.round(price * 100) / 100;
            var dec = Math.round((price % 1) * 100);
            return price + (dec ? '' : '.0') + (dec%10 ? '' : '0');
        }

        $(oe_website_sale).off('change', 'input.js_product_change');
        
        $(oe_website_sale).on('change', 'input.js_product_change', function (ev) {
            var $parent = $(this).closest('.js_product');
            $parent.find(".oe_default_price:first .oe_currency_value").html( price_to_str(+$(this).data('lst_price')) );
            $parent.find(".oe_price:first .oe_currency_value").html(price_to_str(+$(this).data('price')) );
            update_product_image(this, +$(this).val());
        });
        
        $(oe_website_sale).off('change', 'input.js_variant_change, select.js_variant_change, ul[data-attribute_value_ids]');
        
        $(oe_website_sale).on('change', 'input.js_variant_change, select.js_variant_change, ul[data-attribute_value_ids]', function (ev) {
            var $ul = $(ev.target).closest('.js_add_cart_variants');
            var $parent = $ul.closest('.js_product');
            var $product_id = $parent.find('input.product_id').first();
            var $price = $parent.find(".oe_price:first .oe_currency_value");
            var $default_price = $parent.find(".oe_default_price:first .oe_currency_value");
            var $optional_price = $parent.find(".oe_optional:first .oe_currency_value");
            var variant_ids = $ul.data("attribute_value_ids");
            var values = [];
            $parent.find('input.js_variant_change:checked, select.js_variant_change').each(function () {
                values.push(+$(this).val());
            });

            $parent.find("label").removeClass("text-muted css_not_available");

            var product_id = false;
            for (var k in variant_ids) {
                if (_.isEmpty(_.difference(variant_ids[k][1], values))) {
                    $price.html(price_to_str(variant_ids[k][2]));
                    $default_price.html(price_to_str(variant_ids[k][3]));
                    if (variant_ids[k][3]-variant_ids[k][2]>0.2) {
                        $default_price.closest('.oe_website_sale').addClass("discount");
                        $optional_price.closest('.oe_optional').show().css('text-decoration', 'line-through');
                    } else {
                        $default_price.closest('.oe_website_sale').removeClass("discount");
                        $optional_price.closest('.oe_optional').hide();
                    }
                    product_id = variant_ids[k][0];
                    break;
                }
            }

            if (product_id) {
                update_product_image(this, product_id);
            }

            $parent.find("input.js_variant_change:radio, select.js_variant_change").each(function () {
                var $input = $(this);
                var id = +$input.val();
                var values = [id];

                $parent.find("ul:not(:has(input.js_variant_change[value='" + id + "'])) input.js_variant_change:checked, select").each(function () {
                    values.push(+$(this).val());
                });

                for (var k in variant_ids) {
                    if (!_.difference(values, variant_ids[k][1]).length) {
                        return;
                    }
                }
                $input.closest("label").addClass("css_not_available");
                $input.find("option[value='" + id + "']").addClass("css_not_available");
            });

            if (product_id) {
                $parent.removeClass("css_not_available");
                $product_id.val(product_id);
                $parent.find(".js_check_product").removeAttr("disabled");
            } else {
                $parent.addClass("css_not_available");
                $product_id.val(0);
                $parent.find(".js_check_product").attr("disabled", "disabled");
            }
        });
    });
});

That I think that is the one choice you could do if you don't want to use the first choice to provide a new version of the whole file recommended in this case

Hope this help you