One way to hold this word: something thick pushing its way out, very slowly — honey, melted cheese, wet mud — coming through a small gap or through a soft surface. There is no splash and no noise, and it does not stop after one go. Just two feelings: slow, and thick.
From the word’s history
Wiktionary traces the verb and the slow-flow noun to Middle English wose, from Old English wōs, meaning sap or froth: the sticky stuff that seeps out of a plant. It records the mud noun as a separate word, Old English wāse, meaning mud or mire.
維基詞典把動詞 ooze 這條線追到中古英語 wose、古英語 wōs，意思是「樹液、泡沫」，也就是從植物身上慢慢滲出來的黏汁。這正好對上今天「慢慢滲出」的意思。至於「軟泥」那個名詞，同一份資料記的是另一個來源：古英語 wāse（泥、沼澤）。兩個字後來拼成同一個樣子。
Wiktionary (kaikki extract) entry ooze, etymology 1 and etymology 2, as supplied in this evidence packet
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