The best course of action
The information in this answer is my personal interpretation only, so I recommend getting in touch with your local or district authority (They should be considered an essential service at this time), who will be able to make recommendations and advise you the best course of action.
Impounding Act 1955
The Impounding Act 1955 appears to be the relevant legislation, and it appears that you may Impound, but not destroy, the stock. There is a great amount of information and detail in the Act that I will not quote here, but I encourage you to read the relevant parts.
Section 21 of the 'Impounding Act 1955' states
The occupier of any land may seize and impound any stock trespassing
on the land.
Reading further into Part 5 (Sections 21-31) we can see some remedies including section 22(1):
Except as hereinafter provided, stock shall be impounded in the
nearest accessible pound to the place where the stock was found
trespassing.
Section 24 has additional information on impounding the stock on your land if the owner of the stock is known to you.
Note, your local authority can notify you of where to find the closest pound.
In response to your question:
Am I legally entitled to kill the sheep
No, refer to section 31 which does not make allowances for sheep. I have not quoted it here because there are a number of special requirements, refer to the Act for more information.
In response to your question:
am I at liberty to sell the sheep
No, it appears that there are no allowances for private landowners to do so, but it appears that local authority may. However, it does appear that you may seek damages from the stock owner in some situations where fencing was not adequate as per section 26:
(1) Except as otherwise provided in this Act, the occupier of land
trespassed upon by stock shall not be entitled to demand or recover
any damages whatsoever on account of the trespass thereon of any stock
unless—
(a) the land or the portion of the land trespassed upon is fenced; or
(b) he proves that the trespass on to his land was not wholly or
partly due to the fact that his land or the portion trespassed upon
was not fenced; or
(c) in any case where stock trespassing on any land
adjoining his land and not fenced therefrom has trespassed on to his
land from that adjoining land, he proves that the trespass on to the
adjoining land was not wholly or partly due to the fact that that
adjoining land was not fenced; or
(d) the land (whether fenced or
unfenced) is situated in a city or a part of a district that was
formerly a city or borough:
provided that nothing in this paragraph shall apply with respect to
the trespass by stock on to unfenced land having a frontage to a road
declared by the local authority by bylaw to be a stock route, if the
stock is being driven along the road at the time and subject to the
conditions prescribed by the bylaw.
Note sub section 3 as well:
(3) Where stock has been impounded for trespass and the occupier of the
land trespassed upon notifies the poundkeeper that he intends to claim
actual damages instead of trespass rates pursuant to section 27, the
poundkeeper shall, on payment of all other authorised fees and
charges, release the stock to the owner.
Further reading
Link to the Impounding Act 1955: http://www.legislation.govt.nz/act/public/1955/0108/latest/whole.html
