For a testament - Such an arrangement as God enters into with man; see the remarks on Hebrews 9:16.
Is of force - Is ratified, or confirmed - in the same way as a deed or compact is confirmed by affixing a seal.
After men are dead - ἐπὶ νεκροῖς epi nekrois. "Over the dead." That is, in accordance with the view given above, after the animal is dead; or over the body of the animal slain for sacrifice, and to confirm the covenant. "For a covenant is completed or confirmed over dead sacrifices, seeing it is never of force as long as the victim set apart for its ratification is still living." ms. notes of Dr. JohnP. Wilson. To this interpretation it is objected, that "νεκροῖς nekrois - "nekrois" - means only "dead men;" but human beings surely were not sacrificed by the Jews, as a mediating sacrifice in order to confirm a covenant." Prof. Stuart in loc. In regard to this objection, and to the proper meaning of the passage, we may remark:
(1) that the word "men" is not in the Greek, nor is it necessarily implied, unless it be in the use of the Greek word rendered "dead." The proper translation is, "upon, or over the dead." The use of the word "men" here by our translators would seem to limit it to the making of a will.
(2) it is to be presumed, unless there is positive proof to the contrary, that the Greeks and Hebrews used the word "dead" as it is used by other people, and that it "might" refer to deceased animals, or vegetables, as well as to human beings. A sacrifice that had been offered was dead; a tree that had fallen was dead; an animal that had been torn by other wild animals was dead. It is "possible" that a people might have one word to refer to "dead men," and another to "dead animals," and another to "dead vegetables:" but what is the evidence that the Hebrews or the Greeks had such words?
(3) what is the meaning of this very word - νεκρός nekros - "nekros" - in Hebrews 6:1; Hebrews 9:14, of this very Epistle when it is applied to works - "dead works" - if it never refers to anything but people? compare James 2:17, James 2:20, James 2:26; Ephesians 2:1, Ephesians 2:5; Revelation 3:1. In Ecclesiastes 9:4, it is applied to a dead lion. I suppose, therefore, that the Greek phrase here will admit of the interpretation which the "exigency of the place" seems to demand, and that the idea is, that a covenant with God was ratified over the animals slain in sacrifice, and was not considered as confirmed until the sacrifice was killed.
Otherwise - Since - ἐπεί epei. That is, unless this takes place it will be of no force.
It is of no strength - It is not "strong" - ἰσχύει ischuei - it is not confirmed or ratified. "While the testator liveth." Or while the animal selected to confirm the covenant is alive. It can be confirmed only by its being slain. A full examination of the meaning of this passage Hebrews 9:16-17 may be found in an article in the Biblical Repository, vol. 20, pp. 51-71, and in Prof. Stuart's reply to that article. Bib. Repos. 20, pp. 356-381.

For a testament is of force after men are dead,.... The necessity of Christ's death is here urged, from the nature and force of a testament or will, among men, which does not take place, and cannot be executed, till a man is dead.
Otherwise it is of no strength at all whilst the testator liveth; no claim can be made by the legatees for the part they have in it, nor can any disposition be made by the executor of it; not that hereby is suggested, that the testament or will of God was uncertain and precarious till the death of Christ, and subject to change and alteration as men's wills are till they die; nor that the inheritance could not be enjoyed by the Old Testament saints; for it is certain, it was entered upon by them before the death of Christ; but the sense is, that there was a necessity of it, that the saints right unto it, upon the foot of justice, might be evident by it.

after--literally, "over," as we say "upon the death of the testators"; not as THOLUCK, "on the condition that slain sacrifices be there," which the Greek hardly sanctions.
otherwise--"seeing that it is never availing" [ALFORD]. BENGEL and LACHMANN read with an interrogation, "Since, is it ever in force (surely not) while the testator liveth?"

After he is dead - Neither this, nor after men are dead is a literal translation of the words. It is a very perplexed passage.