On sale order, currency_id is a related field based on pricelist_id so you could use pricelist_id, or you could create a new module, inherit sale.order and override the field to make it stored.  I think a simple store=True would be fine as the currency on a price list is unlikely to change.

On Invoices, create a new view in your module, inherit from the invoice search view and add the currency_id in as a group by.

       <record id="view_my_module_account_invoice_search" model="ir.ui.view">
            <field name="name">my.module.account.invoice.search</field>
            <field name="model">account.invoice</field>
            <field name="inherit_id" ref="account.view_account_invoice_filter"/>
            <field name="arch" type="xml">
                <xpath expr="//group/filter[@string='Due Date']" position="after">
                    <filter string="Currency" domain="[]" context="{'group_by':'currency_id'}"/>
                </xpath>
            </field>
        </record>