I've tried that too, a couple of times. Didn't help. The funny thing is, after I remove all the website data it's empty (as it should be) but after I relaunch Safari it immediately gets filled with strange websites I never visit.
Oh, and these are not pop ups, they're just weird ads that show in places they shouldn't be on different websites, but not in another window. Here's an example, a weird banner that never appeared before on a Tidal landing page:

Here's my report:
EtreCheck version: 2.9.12 (265)
Report generated 2016-05-18 22:22:51
Download EtreCheck from https://etrecheck.com
Runtime 2:42
Performance: Excellent
Click the [Support] links for help with non-Apple products.
Click the [Details] links for more information about that line.
Problem: Other problem
Description:
Adware
Hardware Information: ⓘ
iMac (21.5-inch, Late 2013)
[Technical Specifications] - [User Guide] - [Warranty & Service]
iMac - model: iMac14,3
1 2.9 GHz Intel Core i5 CPU: 4-core
8 GB RAM Upgradeable - [Instructions]
BANK 0/DIMM0
4 GB DDR3 1600 MHz ok
BANK 1/DIMM0
4 GB DDR3 1600 MHz ok
Bluetooth: Good - Handoff/Airdrop2 supported
Wireless: en1: 802.11 a/b/g/n/ac
Video Information: ⓘ
NVIDIA GeForce GT 750M - VRAM: 1024 MB
iMac 1920 x 1080
System Software: ⓘ
OS X Yosemite 10.10.5 (14F1808) - Time since boot: about 3 hours
Disk Information: ⓘ
APPLE HDD HTS541010A9E662 disk0 : (1 TB) (Rotational)
EFI (disk0s1) <not mounted> : 210 MB
Macintosh HD (disk0s2) / : 999.35 GB (937.06 GB free)
Recovery HD (disk0s3) <not mounted> [Recovery]: 650 MB
USB Information: ⓘ
Apple Inc. BRCM20702 Hub
Apple Inc. Bluetooth USB Host Controller
Apple Inc. FaceTime HD Camera (Built-in)
Thunderbolt Information: ⓘ
Apple Inc. thunderbolt_bus
Gatekeeper: ⓘ
Mac App Store and identified developers
Kernel Extensions: ⓘ
/Library/Application Support/Avast/components/fileshield/unsigned
[loaded] com.avast.AvastFileShield (3.0.0 - SDK 10.10 - 2016-04-12) [Support]
/Library/Application Support/Avast/components/proxy/unsigned
[loaded] com.avast.PacketForwarder (2.1 - SDK 10.10 - 2016-04-12) [Support]
System Launch Agents: ⓘ
[not loaded] 5 Apple tasks
[loaded] 144 Apple tasks
[running] 63 Apple tasks
System Launch Daemons: ⓘ
[not loaded] 47 Apple tasks
[loaded] 135 Apple tasks
[running] 80 Apple tasks
Launch Agents: ⓘ
[not loaded] com.adobe.AAM.Updater-1.0.plist (2016-05-16) [Support]
[failed] com.adobe.ARMDCHelper.cc24aef4a1b90ed56a...plist (2016-05-10) [Support]
[running] com.adobe.AdobeCreativeCloud.plist (2016-02-14) [Support]
[running] com.avast.update-agent.plist (2016-05-18) [Support]
[loaded] com.avast.userinit.plist (2016-05-18) [Support]
Launch Daemons: ⓘ
[loaded] com.adobe.ARMDC.Communicator.plist (2016-05-10) [Support]
[loaded] com.adobe.ARMDC.SMJobBlessHelper.plist (2016-05-10) [Support]
[running] com.adobe.adobeupdatedaemon.plist (2016-04-12) [Support]
[loaded] com.adobe.agsservice.plist (2016-04-12) [Support]
[loaded] com.adobe.fpsaud.plist (2016-05-10) [Support]
[loaded] com.avast.init.plist (2016-05-18) [Support]
[loaded] com.avast.uninstall.plist (2016-05-18) [Support]
[loaded] com.avast.update.plist (2016-05-18) [Support]
[loaded] com.malwarebytes.MBAMHelperTool.plist (2016-05-18) [Support]
User Launch Agents: ⓘ
[loaded] com.adobe.AAM.Updater-1.0.plist (2015-05-05) [Support]
[not loaded] com.avast.home.userinit.plist (2016-05-18) [Support]
[loaded] com.spotify.webhelper.plist (2015-12-30) [Support]
User Login Items: ⓘ
iTunesHelper program (/Applications/iTunes.app/Contents/MacOS/iTunesHelper.app)
AdobeResourceSynchronizer program Hidden (/Applications/Adobe Acrobat DC/Adobe Acrobat.app/Contents/Helpers/AdobeResourceSynchronizer.app)
Caffeine program (/Applications/Caffeine.app)
Other Apps: ⓘ
[running] com.adobe.CCLibrary.120164
[running] com.adobe.CCXProcess.124708
[running] com.adobe.acc.AdobeDesktopService.67624.630B3942-6941-4A52-9926-090A3D950389
[running] com.adobe.accmac.66204
[loaded] com.avast.account
[loaded] com.avast.crashreport
[running] com.avast.daemon
[running] com.avast.fileshield
[running] com.avast.helper
[running] com.avast.proxy
[running] com.avast.service
[running] com.hp.devicemonitor
[running] com.lightheadsw.caffeine.105396
[loaded] 372 Apple tasks
[running] 181 Apple tasks
Internet Plug-ins: ⓘ
AdobeAAMDetect: 3.0.0.0 - SDK 10.9 (2016-04-12) [Support]
FlashPlayer-10.6: 21.0.0.242 - SDK 10.6 (2016-05-12) [Support]
QuickTime Plugin: 7.7.3 (2016-05-18)
AdobePDFViewerNPAPI: 15.016.20039 - SDK 10.11 (2016-05-13) [Support]
AdobePDFViewer: 15.016.20039 - SDK 10.11 (2016-05-13) [Support]
Flash Player: 21.0.0.242 - SDK 10.6 (2016-05-12) [Support]
Default Browser: 600 - SDK 10.10 (2015-08-18)
3rd Party Preference Panes: ⓘ
Flash Player (2016-05-10) [Support]
Time Machine: ⓘ
Time Machine not configured!
Top Processes by CPU: ⓘ
4% WindowServer
2% fontd
1% Creative Cloud
1% kernel_task
0% com.avast.daemon
Top Processes by Memory: ⓘ
711 MB kernel_task
451 MB com.apple.WebKit.WebContent(6)
254 MB com.avast.daemon
164 MB mdworker(12)
156 MB mds_stores
Virtual Memory Information: ⓘ
1.14 GB Free RAM
6.85 GB Used RAM (3.51 GB Cached)
0 B Swap Used
Diagnostics Information: ⓘ
May 18, 2016, 07:01:15 PM Self test - passed