Right Hand

Alas, the search I did in the OED online has vanished... and I can't find the relevant passages in the paper OED. But the OED entry for 'right hand' lists a number of distinct senses:

1.a. That hand which is nornally the stronger of the two
1.b. [transf.] as a symbol of friendship or alliance
1.c. a person of usefulness or importance; an efficient or indispensable helper or aid
2.c. the position of honour

and it's possible to reconstruct something of the sense from this evidence.

If we want to take the subject further it's useful to realize that "God's Right Hand" is an image from the Bible and look into the reference sources that can help us unpack Biblical allusions. The Interpreter's Dictionary of the Bible [REF 440.I63] says

RIGHT HAND. The side or direction, as well as the hand itself; often used in a figurative sense... the OT and the NT assign special significance to the right hand as the hand of strength (Job 40:14; Ps. 45:4; cf. Luke 6:6; Acts 3:7), the hand of blessing and unique capacity...while the left hand is unusually deceptive and deadly...
The "right hand of God" is the OT metaphor of his mighty power by which he creates, wages war, and delivers his people... Ps. 110:1 is the normative passage... quoted or echoed many times in the NT as a virtually constant element of the apostolic witness to he exalted Christ, reigning in honor and power at the right hand of God (vol 4: 80)

The Anchor Bible Dictionary [REF BS440.A54] adds

...the right hand was the hand of special blessing... In a related usage, the position of honor is regularly at the host's right hand... (vol 5: 724)