I would order my cause before him - Compare the notes at Isaiah 43:26. That is, I would arrange my arguments, or plead my cause, as one does in a court of justice. I would suggest the considerations which would show that I am not guilty in the sense charged by my friends, and that notwithstanding my calamities, I am the real friend of God.
And fill my mouth with arguments - Probably he means that he would appeal to the evidence furnished by a life of benevolence and justice, that he was not a hypocrite or a man of distinguished wickedness, as his friends maintained.

I would order my cause before him,.... Either, as a praying person, direct his prayer to him, and set it in order before him, see Psalm 5:3; or else as pleading in his own defence, and in justification of himself; not of his person before God, setting his works of righteousness in order before him, and pleading his justification on the foot of them; for, by these no flesh living can be justified before God; but of his cause, for, as a man may vindicate his cause before men, and clear himself from aspersions cast upon him, as Samuel did, 1-Samuel 12:5; so he may before God, with respect to the charges he is falsely loaded with, and may appeal to him for justice, and desire he would stir up himself, and awake to his judgment, even to his cause, and plead it against those that strive with him, as David did, Psalm 35:1;
and fill my mouth with arguments; either in prayer, as a good man may; not with such as are taken from his goodness and righteousness, but from the person, office, grace, blood, righteousness, and sacrifice of Christ, and from the declarations of God's grace, and the promises of his word; or else as in a court of judicature, bringing forth his strong reasons, and giving proofs of his innocence, such as would be demonstrative, even convincing to all that should hear, and be not only proofs for him, and in his favour, but reproofs also, as the word (c) signifies, to those that contended with him.
(c) "increpationibus", V. L. and so Montanus, Beza, Mercerus, Drusius, Schultens.

order--state methodically (Job 13:18; Isaiah 43:26).
fill, &c.--I would have abundance of arguments to adduce.