Paul knew about the logia

The words "persuasive words of wisdom" (πειθοις σοφιας λογοις 1 Cor 2:4) make a very apt description of the logia as a whole. For as R. E. Murphy pointed out: "Jesus is presented in the synoptic Gospels as a wisdom teacher ... The many logia (sayings) attributed to him are cast in the aphoristic style of the sages ..." [1]
There are also many allusions to its individual sayings. Here are two good examples:
(1) "the Lord commanded that those who proclaim the gospel should get their living by the gospel" (1 Cor 9:14, c.f. "the worker deserves his pay" in saying B4, where the context shows that the "worker" is a missionary)
(2) "the day of the Lord will come like a thief in the night ... keep awake" (1 Thess 5:2,6, c.f. "Keep awake ... day your master is coming ... time of night the thief was coming" in saying D14).

1 Cor chs. 1-4

These chapters contain the biggest concentration of references/allusions. It seems likely that Paul was annoyed by the logia-based preaching of someone in Corinth (perhaps Peter) who followed Jesus but didn't accept the gospel as set out by Paul.

(3) "wisdom ... preach ... Jews demand signs" (1 Cor 1:21-23a, c.f. "It is an evil generation which demands a sign ... the wisdom of Solomon ... the preaching of Jonah" in saying C5)
(4) "consider your call", followed by the threefold repetition of "not many" and "God chose" (1 Cor 1:26-29, c.f. saying C2: "Many are called, but few are chosen")
(5) 1:8, day of our/the Lord, c.f. D12
(6) 1:17, words of wisdom, a veiled reference to the logia as a whole
(7) 1:20b,25a, wise & foolish, c.f. A22
(8) 2:1, lofty words or wisdom, again hinting at the logia
(9) 2:4, plausible words or wisdom, again hinting at the logia
(10) 2:5, human wisdom, again hinting at the logia
(11) 3:5, on being a servant, c.f. C10
(12) 3:11, building on a sound foundation, c.f. A22
(13) 4:5, hidden things brought to light, c.f. B9
(14) 4:8, satisfied, poor, king(dom), c.f. the first two blessings in A1
(15) 4:9, a spectacle to angels and men, c.f. B9
(16) 4:10, another reference to wise & foolish, c.f. A22
(17) 4:11, hungry, c.f. A1
(18) 4:12, reviled, c.f. A1
(19) 4:12, endure, c.f. B6
(20) 4:20, the kingdom does not consist in words (as in the logia?!)
(21) 4:20, kingdom of God & power, c.f. C12
(22) 4:21, staff, c.f. B4

Other allusions:

(23) Rom 6:6, take up cross / crucified with Christ, c.f. B11
(24) Rom 12:14, bless / pray for those who persecute you, c.f. A8
(25) Rom 14:13a, do not judge others, c.f. A14
(26) Rom 14:13b, stumbling block, c.f. C9
(27) Rom 14:17, the kingdom of God is not food and drink, c.f. C19
(28) Rom 14:17, the kingdom of God is ... peace ..., c.f. B10
(29) 1 Cor 5:6, yeast ferments, c.f. C14
(30) 2 Cor 11:20, being struck on the face, c.f. A8
(31) Gal 4:4-5a, the mission to Jews, c.f. B4
(32) Gal 4:6, God as Father (Abba), c.f. C1
(33) Php 1:6,10, day of Christ / Son of Man, c.f. D12
(34) Php 2:8-9, humble exalted, c.f. C11
(35) Php 4:5, Lord /kingdom of God is getting near, c.f. B4
(36) 1 Thess 5:14, be devoted to the weak / the one, c.f. C16

References

1. P. J. Achtemeier (Ed.), "The HarperCollinsBible Dictionary" (HarperSanFrancisco, 1996, p.1215)