Lexical Definition

‎στρατεία‎ strateía (strat-i'-ah) warfare ^G:N-F
from ‎στρατεύομαι‎

warfare.

• military service, i.e. (figuratively) the apostolic career (as one of hardship and danger)

Abbott-Smith

στρατεία (on the orthogr., v. Deiss., BS, 181 f.), -ας, ἡ (< στρατεύω), [in LXX chiefly for צָבָא ;]
an expedition, a campaign, warfare: metaph., II Co 10:4 (-τιά, T), I Ti 1:18.†

Abbott-Smith References

Liddell-Scott-Jones

στρατεία,

Ionic dialect -ηΐη, ἡ, (στρατεύω) expedition, campaign, στρατηΐην ποιεῖσθαι ἐς.., ἐπὶ.., [Refs 5th c.BC+]; ἀπὸ στρατείας coming from war, after service done, [Refs 4th c.BC+]; κατὰ τὴν Σιτάλκου σ. about the time of his expedition, [Refs 5th c.BC+]; ἐπὶ στρατείας εἶναι to be on foreign service, [Refs 5th c.BC+]; so ἐν στρατείᾳ ὄντας [Refs 5th c.BC+]; ἐν τῇ σ. [Refs 3rd c.BC+]; παραγγέλλειν τινὶ σ. κατὰ γῆν [Refs 5th c.BC+]; στρατείαν ξυνεξελθεῖν[Refs 4th c.BC+]; τῆς σ. γιγνομένης ἐκ καταλόγου [Refs 4th c.BC+]; frequently in plural, military service, warfare, [Refs 5th c.BC+]; πρὸς ταῖς αὑτοῦ σ. in addition to the campaigns which he is bound to serve, [Refs 4th c.BC+]; στρατείας στρατεύεσθαι [Refs]; ἀφειμένος στρατείας, = Latin exauctoratus, [Refs 1st c.AD+]

__2 σ. ἐν τοῖς ἐπωνύμοις levy of those liable to serve in the year of such and such archons, [Refs 4th c.BC+]
__3 σ. ἡ ἐν τοῖς μέρεσιν expedition for special service, to train the young soldiers next after serving as περίπολοι, [Refs 4th c.BC+]
__4 military discipline, ἡ ἀκριβὴς σ. [Refs 2nd c.AD+]
__5 military appointment, ἐπώλησε στρατείας [Refs] —στρατιά is a constant variant, and is sometimes undoubtedly used= στρατεία (campaign), see at {στρατιά} [Refs 5th c.BC+]; but στρατεία= army, expeditionary force is very rare, [Refs 5th c.BC+] never = army, but both -εία [Refs 3rd c.BC+] = campaign.