Admittedly this isn't Homer, but it might still be useful. A TLG search (surprisingly) comes up with only two relevant sentences, both from Plato:
Theaetetus 204b-c has the numbers up to six in the neuter gender:
ἕν, δύο, τρία, τέτταρα, πέντε, ἕξ
One, two, three, four, five, six
Timaeus 17a counts up to three with the masculine gender:
εἷς, δύο, τρεῖς: ὁ δὲ δὴ τέταρτος
One, two, three; but the fourth...
(Proclus' commentary tells us that Plato was heavily criticized for switching from cardinal to ordinal numerals here.)
I don't see this dealt with in grammars, but it seems that in Theaetetus, Plato uses the neuter forms because he is counting abstract numbers, whereas in Timaeus he uses the masculine forms because he is counting men. (And so if he were counting women, we might expect to see the feminine forms.) So if my interpretation is correct, you would count things depending on what gender they have, or in the neuter gender for abstract counting.
In Homeric Greek, of course, the numbers have to be changed to match Homer's dialect, so use τέσσαρα/τέσσαρες instead of τέτταρα/τέτταρες. δύω can also be used in Homer instead of δύο.
Masculine: εἷς δύο τρεῖς τέσσαρες
Feminine: μία δύο τρεῖς τέσσαρες
Neuter: ἕν δύο τρία τέσσαρα
5-10 (all genders): πέντε ἕξ ἑπτά ὀκτώ ἐννέα δέκα