For 或, what semantic notions underlie "tool or weapon on a pole" (戈) + "mouth" (口) + "territory" (1)?
There is a misunderstanding on the Wiktionary description, which shouldn't have inappropriately linked 口 and 一; these are listed for their shapes rather than their functions. The description

Ideogrammic compound (會意): 戈 + 口 + 一, “territory”.

means the separate parts which look like 戈 + 口 + 一 are combined together into one glyph to mean territory. The two meaningful components to take note of are 「戈」 (picture of a dagger-axe) and 「囗」 or 「丁」 (picture of fortifications surrounding a settlement).
Territory is now written with the derivatives

「國」 (region, country), through the addition of another semantic 「囗」
「域」 (territory, region), through the addition of semantic 「土」 (earth, soil)


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「或」 was originally a compound of 「戈」 (dagger-axe, representing military power) guarding 「囗」 or 「丁」 (picture of fortifications surrounding a settlement; see Characters&#39; original forms that have no independent usage for further discussion). The original idea was basically that of a defended settlement.
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Some variants added strokes surrounding 「囗」 or 「丁」, emphasising the region's boundaries. Compare 「疆」 (originally field boundaries (畕), with lines added surrounding the fields later) or 「畫」 (to draw the line between fields (田), now written 「劃」).

Early on, 「或」 became used for a phonetic loan meaning someone, something. The meaning either, or is a semantic extension of this phonetic loan meaning. Schuessler suggests that this meaning of 「或」 (Baxter-Sagart OC: /*[ɢ]ʷˤək/) is etymologically related to 「有」 (/*[ɢ]ʷəʔ/, there is, exists). The other senses are either further semantic extensions or from compound words like

或許 (maybe)
間或 (occassionally, sometimes)