(But I would strengthen you with my mouth With that which proceeds from the mouth - words.
And the moving of my lips - My speaking - implying that it would have been done in a mild, gentle, kind manner - so that the lips would appear just to move. Others, however, have given a different interpretation. Thus, Dr. Good renders it:
"With my own mouth will I overpower you,
Till the quivering of my lips shall fall."
But the common interpretation is to be preferred. The word rendered "moving" ניד nı̂yd is from נוּד nûd - "to move," "agitate," and hence, denotes "motion." It denotes here the motion of the lips when we speak. Gesenius renders it, "consolation," "comfort" - because this is expressed by a motion of the head.
Should assuage your grief - The word used here (יחשׂך yachâśak) means properly "to hold back," "to restrain;" Job 7:11. Here it is correctly rendered, meaning that he would hold back, or check their sorrows. In other words, he would sustain them.

I would strengthen you with my mouth - Mr. Good translates thus: -
"With my own mouth will I overpower you,
Till the quivering of my lips shall fail;"
for which rendering he contends in his learned notes. This translation is countenanced by the Septuagint, Syriac, and Arabic versions.

[But] I would strengthen you (e) with my mouth, and the moving of my lips should asswage [your grief].
(e) If this were in my power, yet I would comfort you and not do as you do to me.

But I would strengthen you with my mouth,.... Comfort them with the words of his mouth; so God strengthens his people with strength in their souls, when he answers them with good and comfortable words; an angel strengthened Christ as man when in an agony, comforting him, suggesting comfortable things to him; so one saint may strengthen and comfort another when in distress, whether of soul or body; see Psalm 138:3; and thus Job had strengthened and comforted others, with his words in former times, as Eliphaz himself owns, Job 4:3 and so he would again, were there a change in his circumstances, and objects presented:
and the moving of my lips should assuage your grief: words uttered by him, which are done by the moving of the lips, should be such as would have a tendency to allay grief, to stop, restrain, forbid, and lessen sorrow; at least that it might not break out in an extravagant way, and exceed bounds, and that his friends might not be swallowed up with overmuch sorrow.

strengthen . . . with . . . mouth--bitter irony. In allusion to Eliphaz' boasted "consolations" (Job 15:11). Opposed to strengthening with the heart, that is, with real consolation. Translate, "I also (like you) could strengthen with the mouth," that is, with heartless talk: "And the moving of my lips (mere lip comfort) could console (in the same fashion as you do)" [UMBREIT]. "Hearty counsel" (Proverbs 27:9) is the opposite.