The return of the commissioners, made at their next regular statute session after the hearing provided for in section 2054, shall be placed on file and remain in the custody of their clerk for inspection without record. The case shall be continued to their next regular term of record, and at any time on or before the 3rd day thereof, if no appeal from the location be taken, all persons aggrieved by their estimate of damages shall file their notice of appeal. If no such notice is then presented or pending, the proceedings shall be closed, recorded and become effectual; all claims for damages not allowed by them be forever barred; and all damages awarded under sections 2051 to 2061, 2101, 2151 and 2152 paid out of the county treasury except as provided in section 2101. If an appeal from the location be taken in accordance with section 2063, then notice of appeal on damages may be filed with the clerk of the county commissioners within 60 days after the final decision of the appellate court in favor of such way as has been certified to him, to the Superior Court in the county where the land is situated, which court shall determine the same in the same manner as is provided in section 2058, when no appeal on location is taken.