Couldn't find a c# example so I created one.  A customer wanted to pull notes from an Invoice to place in SAGE when the processing orders were being pulled down via the v2 API.

//pass in the order_id value from your salesOrderEntity object.

 public salesOrderInvoiceEntity[] GetSalesOrders(string orderID)
        {
            if (string.IsNullOrEmpty(this.SessionId))
                this.Login();

            filters listFilters = null;

            complexFilter cFilter = new complexFilter();

            cFilter.key = "order_id";
            cFilter.value = new associativeEntity
            {
                key = "equal",
                value = orderID
            };

            listFilters = new filters();
            listFilters.complex_filter = new complexFilter[] { cFilter };

            salesOrderInvoiceListRequest req = new salesOrderInvoiceListRequest(this.SessionId, listFilters);
            return magentoService.salesOrderInvoiceList(req).result;
        }

//I Only need the last comment but you can return the salesOrderInvoiceCommentEntity object and parse all that the invoice has.
  public string  GetInvoiceComments(string id)
        {
            if (string.IsNullOrEmpty(this.SessionId))
                this.Login();
            salesOrderInvoiceInfoResponse req = magentoService.salesOrderInvoiceInfo(new salesOrderInvoiceInfoRequest(this.SessionId, id));
            if (req.result.comments != null)
                return req.result.comments[0].comment;
            else
                return string.Empty;

        }