For later reference, here’s a collection of etymologically opaque (to me) Eastern Votic words harvested from my new dictionary. I will not attempt any detailed analysis yet. (Presumably some investigation into Russian, Ingrian, Estonian, maybe even Latvian & German could turn up known cognates for many of these.)
[Edit 2016-03-16: several comparisons have been provided in the comments, and these words have now been struck out.]
aimo ‘carbon monoxide’- alëtsë ‘mitten’
hilkeä ‘ugly’ — if this is not a hypercorrect cognate of Finnish ilkeä ‘evil’.- hulkkuag ‘to travel’
hülpeä ‘disobedient’- ikolookka ‘rainbow’ — a compound based on lookka ‘bow, curve’, but the 1st element is unclear.
jahsaag ‘to take off shoes’ — does not seem related to Finnish jaksaa ‘to have energy for’.- kaaliag ‘to lick’
- kaputta ‘sock’
- kineri ‘melted fat’
- koltši ‘old-fashioned ladle’
kosma ‘hair’- lainatag ‘to swallow’ — does not seem related to Finnish lainata ‘to borrow’.
- lautta ‘cowshed’ — does not seem related to Finnish lautta ‘raft’.
- liblo ‘oat awn’
- linnaasëd ‘malt’
- lohko ‘soup’
- lühtši : lühdže- ‘pail’
- läntü ‘milk’
- mauttši ‘intestine’
- naka ‘cask spigot’
- nakliska ‘some part in a sleigh’ (“the informant is unable to explain what exactly”)
- nëikko ‘rockable cradle’
- nättšelikko ‘burdock’
- nätši ‘uncooked (of bread)’
- nättü ‘rag’
ootava ‘cheap’- pallo ‘pigeon’
- pelssimed ‘loom’
- peltta ‘leftovers of threshing’
- pihta ‘shoulder’
- pilpa ‘dandruff’
- pärähmä ‘fathom, armful’
- raaka ‘twig’
ramitsaag ‘to limp’- ratiz ‘granary’
- rehnüüz ‘entrance hall’
rehtilä ‘griddle’- ringuttaag ‘to stretch’
- ripa ‘footwraps’
- ripila ‘fireplace poker’
rooppa ‘porridge’rootšiag ‘to dig, to rummage’- ruttaag ‘to hurry’
śalko ‘foal’- servä ‘edge’
- sippelikko ‘ant’
- sisava ‘nightingale’
- sultsiag ‘to wash’
- surmukaz ‘relative’ — probably not derived from surma ‘death’?
- säblä ‘kitchen hook’
šitinka ‘bristle’šlotta ‘slush’taari ‘ale’- tahtši : tahdžë- (!) ‘chaff’
- tauttaag ‘to take’
- tiheh ‘mosquito’
- turvaz : turpaa- ‘ladder’
- tuutikko ‘washbundle’
türü ‘food comprising breadcrumbs mixed with milk or water’- tšiutarë ‘coldroom’
- tšiutto ‘shirt’
- tšäppeä ‘beautiful’
- uhër ‘auger’
- unka ‘wooden cup’
- upa ‘bean’ = Est. uba.
- ursi : urtë- ‘bed curtain’
vaattaag ‘to look’- valo ‘dung’
- varo ‘hoop’
- veelatag ‘to soak’ — compound with vete- : vee- ‘water’?
vokki ‘spindle’- väitšiäg ‘to call’
- ördžähtäässäg ‘to wake’
Freelance reconstruction 
A couple of quick notes:
aimo ‘carbon monoxide’ Old Norse eimi, eimur ‘smoke, steam, fire’, Icelandic eimur ‘steam’
jahsaag ‘to take off shoes’ < PU *jaksa- 'take off' (UEW 630; note also Skolt Saami jä´hssed 'take off', a loan from Finnic *jaksa-)
ootava ‘cheap’ ~ Fi dial. huotava
rehtilä 'griddle' ~ Fi riehtilä
śalko ‘foal’ ~ Fi sälkö (but this is a weird vowel correspondence)
vaattaag ‘to look' < Est vaata-, which in turn irregularly from PFi *valvatta-
I can’t find any German ones in there; šlotta looks German, but isn’t. But of course I might have failed to see through simplified consonant clusters.
Some Russian loanwords:
kosma ‘hair’ < космы (pl.) 'mane, dishevelled locks'
ramitsaag ‘to limp’ < ? хромать 'to limp' (an early borrowing, judging by a Russ.o)
rooppa ‘porridge’ < крупа 'groats' (an early borrowing, judging by oo < PSlav. *oo ( Russ. у)
rootšiag ‘to dig, to rummage’ < ? рыться 'to dig, to rummage'
šitinka ‘bristle’ < щетинка 'bristle'
šlotta ‘slush’ < слота 'slush' (a dialect word with cognates in other Slavic languages)
türü ‘food comprising breadcrumbs mixed with milk or water’ < тюря 'id.'
In Finnish dialects we can find:
taari ‘rapakalja’
vokki ‘rukki’
hilkeä & hylpeä < Fi. ilkeä & ylpeä — hypercorrect borrowings.