Eating lobster, clam, oyster and octopus is haram. According to religious resources regarding halal and haram meat, there are general rulings and numerous standards; for instance, a set of rulings has been given for land animals, sea creatures, birds and so on.
The condition for halal meat sea creatures is to have scales.
In a hadith from Imam Baqir (A.S.), Muhammad ibn Muslim asks: “We are given fish that do not bear an extra layer on them (scales)”. The Imam replied: “Eat all fish that have scales and do not eat those that do not.”  According to the ahadith, what is meant by the extra layer is the scales. 
The Great Maraje’ Taqlid have pointed out the ruling of sea creatures based on these traditions.
They state that based on the ahadith, every sea creature is haram except those that have scales. However, shrimp is an exception to this general ruling. We have a special hadith that considers shrimp as an exception: “Eating it (shrimp) is permissible, for it is a kind of fish”. 
Despite the fact that, essentially shrimp don’t have scales, from the legal perspective it is set within the category of fish that have scales. In other words, for reasons we are not aware of, it has been considered as an exception and consequently halal, although it doesn’t have scales. 
In addition, we have a hadith that states the impermissibility of crab:
“Eating jer ī (type of fish), turtle and crab is haram.” 
Therefore, octopus, etc. remain within the general ruling of impermissibility.
One must note that being legally inedible does not make it haram to sell, purchase or catch, because the prohibition of eating something is a complete different thing from the prohibition of selling and purchasing it the same thing. There are cases where a certain thing is haram to eat or drink but can be sold and purchased. For example, blood. It is haram to eat but can be purchased and sold for other benefits. Therefore, purchasing and selling lobster, clam, oyster, etc. in the market, for reasons other than eating like benefiting from the other uses it has, is permissible. Perhaps lobster, clam, etc. have other benefits as well.
 Sheikh Hurr Ameli, Wasa’il al-Shia, vol. 16, pp. 397 and 398, hadith 1 of chapter 8, the chapters on foods and drinks.
 Ibid, hadiths 3 and 7.
 Wasa’il al-Shia ,pg. 408, hadiths 5 and 12, book of foods and drinks.
 Footnote of Wasa’il al-Shia, pg. 408.
 Wasa’il al-Shia , vol. 24, pg. 146, book of foods and drinks, chapter 16, hadith 1.