This would be unlikely, but maybe there's a break in the drain line somewhere. I am now working on an old house in which a portion of the stack had to be replaced due to a crack in a hub (sanitary tee) that was dripping in the wall. Big mess. Probably not your issue, though. But first I would tent everything, separately, with plastic. Let it sit for a while, then slowly remove each and put your nose under to see if you can locate the smell underneath. For example, cover the shower drain. Cover the entire toilet. Cover the sink, etc. I once did this for a bathroom and discovered the stinky smell emanating from the tile & grout itself (I had draped the tile wall with painter's plastic, too.) The smell was due to wet greenboard behind the tile. No kidding.. And it did stink like the sewer. Another time I did this and it turned out to be the sink drain. After pulling out the pop-up drain, we found it covered in black goop from toothpaste spit, hair, etc. Really gross. After cleaning it up, all was well. Yes, that can smell like sewer smell too, if it's been there a while. Good luck. BTW, see if you get the smell when you turn on the sink faucet. If there's gunk in the drain (like just above the trap), the smell will come out of the sink overflow and hit you right in the face. We have this occasionally, and I pour a little splash of bleach down the drain and let it sit. This post was edited by homebound on Wed, Mar 19, 14 at 7:15

Do not be too quick to dismiss your previous plumber for suggesting a AAV (Air Admittance Valve, "studor vent") for your kitchen island. Although the Uniform Plumbing code(UPC) & International Residential Code(IRC)have radically differing views on how a kitchen island vent is to be constructed, nonetheless, both the IRC & UPC do allow an AAV for kitchen island venting. Under the IRC all structures are required to have one "Main Vent",which must run undiminished in size from the structure "Main Drain" through the roof. After that we are permitted to install an unlimited number of AAV's. Under the UPC they do not require a "Main Vent" but all fixture vents are required to be sized by the total DFU (Drainage fixture unit) load of all fixtures served by that vent. Under the UPC a structure is only permitted a maximum of one AAV, with the expressed written consent of the local inspecting authority, and in most cases a kitchen island is the only location where they will grant the exception. Now what is the difference between the kitchen drain and your bathroom drain you ask? When we have a sink on an island it is generally the only fixture attached to that line. As the water drains from the sink it pushes the air ahead of the water in the pipe. Under some circumstances this can result in a slight vacuum in the pipe behind the moving water. This partial vacuum would then result in the standing water in the trap being sucked into the pipe by siphon action and once the water has passed on down the trap is left dry, allowing sewer gas to enter the structure. In this case we install an AAV, which would permit air to enter the pipe behind the liquid flow, thus negating the suction effect. There is a slim chance that you might resolve your problem by installing an AAV on the lavatory drain line, an when you consider the cost of installing an AAV as opposed to opening walls it might be well worth your time to try it, however I suspect you have a different problem in your bathroom. You state that you hear a gurgling sound in the tub or lavatory when another drain is used. It is possible that the water in the gurgling trap is being sucked out, and in that case an AAV might resolve the problem, but I suspect you problem is not a result of negative pressure (the partial vacuum) but rather it result from positive pressure. As the water from one fixture flows through the pipe it pushes the air ahead, causing a slight positive air pressure. Normally that positive pressure would be pushed up and out a roof vent however if your system does not have the required roof vent as one fixture is draining it will push that air up through one of the adjacent fixture drains and out through the trap. Keep in mind that the air in the line contains sewer gas so as that air & sewer gas mix is pushed out you get the odor. The odor may seem greater at some times than others. That does not mean the sewer gas is not leaking because not all the component of sewer gas are odorous. In fact, one of the main gases that comprise sewer gas is totally odorless.

I see one of four potential problems here: 1.Pour about 2 quarts of water in the drain then use a flashlight and look down the drain to see if there is any standing water in the pipe? If you see standing water down in the pipe that is your trap. Hexus mentioned pouring distilled water in the drains to prevent evaporation. I can assure you that will not work because distilled water would evaporate at approximately the same rate as tap water. On the other hand, if you pour about 2oz of vegetable cooking oil in the drain it will float on top of the water and retard evaporation. 2.Examine the floor drain. If it is cast iron and appears to have a center pipe extending up to approximately 1/2" below the floor level and an outer section surrounding that pipe about 2" wide that holds water there is no trap under the drain opening. For those type of floor drains the lid has a pipe section that hangs down into that outer channel. With the lid in place water enters through an outer ring of holes into the outer ring, flows under the section of pipe extending down from the lid, then up and over the center standpipe to enter the drain. If the cap is missing or lost there is no trapping action. (In most jurisdictions we are no longer permitted to install that type of floor drains), 3. Check your furnace to see if you have ducted return air or is the air ducted into the basement then is drawn from the basement into your furnace return air duct. If this is the case you may not have sufficient return air ducting and while the furnace is running it is creating a slight negative air pressure in the basement and the sewer gas is being sucked up through the water in the traps. The solution here is to have dedicated return air ducts installed from the living space above directly to the furnace air return. 4. If you pour water in the traps and top it off with the cooking oil but you are still smelling the sewer gases your basement may be too tight to permit an adequate supply of combustion air for your furnace, water heater and laundry dryer. The code requires that we must find the manufacturers BTU rating on each appliance and add all the BTU values together to get a total BTU/hr rating for all combustion appliances. Code defines a "Confined space" as any space that has less than 50 cubic feet for each 1,000 BTU's. By example furnaces typically range 50-200Kbtu/hr. For the purpose of illustration let us assume the furnace is 100Kbtu plus 35Kbtu for the water heater and another 35Kbtu for a laundry dryer. The total combined BTU/hr rating would then be 170Kbtu per hour. We are required 50cu.ft for each 1kbtu so it would be 50cu.ft x 170 = 8500cu.ft. Now assuming the basement has an 8ft ceiling we have 8500cu.ft / 8'= 1062.5sq.ft. In this example if the room in the basement where the furnace, water heater and dryer are located has less than 1062.5sq.ft it is a "Confined space". The end result of a confined space is that the appliances will produce a negative air pressure, resulting in improper combustion which produces high levels of carbon monoxide. In addition the slight drop in air pressure will result in sucking air down from the living space and both air and sewer gases up through the floor drains. Whenever we determine that the gas appliances are in a "Confined space" we are required to install ducting to allow additional outside air into the machinery space. (The size and placement of the air ducts is also very closely regulated by code.)

".....I have had countless people here and no one can figure out any thoughts would be appreciated" It's not how many you ask that counts,,,,,,,,,it's asking one that knows how to go about it. From firsthand experience I can tell you that locating source of odors can be very tough. Has the intire system been smoke tested? A new house with as many issues as you have already fixed may have countless others,some inside walls. I would be putting a twitch on the builder and/or plumbing sub until it's fixed.