It's a few years since I did GCSE Latin, but with the help of Wiktionary to double-check the declensions I've struggled through all of the listed phrases.
"Colei canis in vacuo": grammatically correct, translates as "The dog's balls in (a) vacuum". If the intention was "The dog's balls in space" then it should probably be "in caelis" (in the heavens) instead of "in vacuo".
"Da da per forcipem": grammatically correct, but somewhat nonsensical. "Give give through forceps"?!
"Ad astra et ad taverna": as commented above, it should be "tabernam" (b, not v; and in the accusative"; and it would be more idiomatic to use -que rather than et. "Ad astra tabernamque": to the stars and the pub.
"In vacuo nemo clamorem audit": grammatically correct; translates as "In a vacuum no-one hears shouting". I'm not sure whether this was intentionally phrased to avoid calls from Ridley Scott's lawyers, or whether the submitter was avoiding the complication of which verb form to use for the object of auditere.
"Pilas ad parietem": I'm not sure what this is trying to say. I has no verb and no subject, just two nouns in the accusative case. If the intended translation was "Mortar to the wall", it might be correct as "Pila ad parietem", but I'm not sure what that has to do with LOHAN.
"Veni vici ballocketi" would be grammatical if there were an irregular second declension noun ballockere. I think I may be missing a cultural reference here.
"Et anatis cum tape XL WD" is nonsense. "And of the duck with" followed by three non-Latin words. I hazard a guess that the intended meaning is "With duck tape and WD-40", which might be translated as "Cum cincta anatis et WD-XL", but the use of "cincta" for "tape" is by working backwards from modern Romance languages. And who knows what the ablative of WD-40 is?
"Pervenientes usque pro stilo cælos in": almost grammatically correct. It's necessary to correct "caelos" (non-existent declension) to "caelis" to get "Those who are arriving all the way in front of a stake to the heavens". I am puzzled by the use of the plural "pervenientes", but I haven't paid enough attention to the LOHAN project to know how many passengers it's carrying.
"Omnes vacuums hereditatem datæ sunt nobis": not grammatical, and it's not obvious how to fix it. "datae sunt nobis" gives a passive verb with actor "us", so it needs a nominative plural: if we correct vacuums (which isn't any of the declined forms of vacuus) to vacui then we can translate as "All voids are given an inheritance by us", but that's not very sensical. The other option for the subject is an implicit "they", but then we need one of the two objects to be a dative, and since "omnes" is plural nominative or accusative and "hereditatem" is singular accusative that's not possible.
"De ebrietate, ingenium" is grammatical: "From drunkenness, intelligence".
"Navis volitans mea plena anguillarum est" is grammatical: "My hovering ship is full of eels".