FFMpeg on Android, undefined references to libavcodec functions, although it is listed on command line

The following Android.mk works for me, including handling the target arch. The result of running the bambuser build.sh is copied from .../build/ffmpeg to /jni/lib/ffmpeg. I'm using PREBUILD_SHARED_LIBRARY rather than PREBUILT_STATIC_LIBRARY as the OP did.

LOCAL_PATH := $(call my-dir)

include $(CLEAR_VARS)
LOCAL_MODULE := libavcodec
LOCAL_SRC_FILES := lib/ffmpeg/$(TARGET_ARCH_ABI)/lib/$(LOCAL_MODULE).so
LOCAL_EXPORT_C_INCLUDES := $(LOCAL_PATH)/lib/ffmpeg/$(TARGET_ARCH_ABI)/include
include $(PREBUILT_SHARED_LIBRARY)

include $(CLEAR_VARS)
LOCAL_MODULE := libavcore
LOCAL_SRC_FILES := lib/ffmpeg/$(TARGET_ARCH_ABI)/lib/$(LOCAL_MODULE).so
LOCAL_EXPORT_C_INCLUDES := $(LOCAL_PATH)/lib/ffmpeg/$(TARGET_ARCH_ABI)/include
include $(PREBUILT_SHARED_LIBRARY)

include $(CLEAR_VARS)
LOCAL_MODULE := libavdevice
LOCAL_SRC_FILES := lib/ffmpeg/$(TARGET_ARCH_ABI)/lib/$(LOCAL_MODULE).so
LOCAL_EXPORT_C_INCLUDES := $(LOCAL_PATH)/lib/ffmpeg/$(TARGET_ARCH_ABI)/include
include $(PREBUILT_SHARED_LIBRARY)

include $(CLEAR_VARS)
LOCAL_MODULE := libavfilter
LOCAL_SRC_FILES := lib/ffmpeg/$(TARGET_ARCH_ABI)/lib/$(LOCAL_MODULE).so
LOCAL_EXPORT_C_INCLUDES := $(LOCAL_PATH)/lib/ffmpeg/$(TARGET_ARCH_ABI)/include
include $(PREBUILT_SHARED_LIBRARY)

include $(CLEAR_VARS)
LOCAL_MODULE := libavformat
LOCAL_SRC_FILES := lib/ffmpeg/$(TARGET_ARCH_ABI)/lib/$(LOCAL_MODULE).so
LOCAL_EXPORT_C_INCLUDES := $(LOCAL_PATH)/lib/ffmpeg/$(TARGET_ARCH_ABI)/include
include $(PREBUILT_SHARED_LIBRARY)

include $(CLEAR_VARS)
LOCAL_MODULE := libavutil
LOCAL_SRC_FILES := lib/ffmpeg/$(TARGET_ARCH_ABI)/lib/$(LOCAL_MODULE).so
LOCAL_EXPORT_C_INCLUDES := $(LOCAL_PATH)/lib/ffmpeg/$(TARGET_ARCH_ABI)/include
include $(PREBUILT_SHARED_LIBRARY)

include $(CLEAR_VARS)
LOCAL_MODULE := libswscale
LOCAL_SRC_FILES := lib/ffmpeg/$(TARGET_ARCH_ABI)/lib/$(LOCAL_MODULE).so
LOCAL_EXPORT_C_INCLUDES := $(LOCAL_PATH)/lib/ffmpeg/$(TARGET_ARCH_ABI)/include
include $(PREBUILT_SHARED_LIBRARY)

include $(CLEAR_VARS)

LOCAL_MODULE    := mynativecode
LOCAL_SRC_FILES := native.c
LOCAL_SHARED_LIBRARIES := libavcore libavdevice libavfilter libavutil libswscale libavformat
LOCAL_LDLIBS := -L$(NDK_PLATFORMS_ROOT)/$(TARGET_PLATFORM)/arch-arm/usr/lib \
                -L$(LOCAL_PATH)/lib/ffmpeg/$(TARGET_ARCH_ABI)/lib \
                -lavcore \
                -lavformat \
                -lavcodec \
                -lavdevice \
                -lavfilter \
                -lavutil \
                -lswscale \
                -llog \
                -lz \
                -ldl \
                -lgcc

include $(BUILD_SHARED_LIBRARY)

I also had to change the bambuser build.sh to modify the --soname-prefix argument to include my package name rather than bambusers.

        FLAGS="--target-os=linux --cross-prefix=arm-linux-androideabi- --arch=arm"
        FLAGS="$FLAGS --sysroot=$SYSROOT"
-       FLAGS="$FLAGS --soname-prefix=/data/data/com.bambuser.broadcaster/lib/"
+       FLAGS="$FLAGS --soname-prefix=/data/data/<my package name here>/lib/"
        FLAGS="$FLAGS --enable-shared --disable-symver"
        FLAGS="$FLAGS --enable-small --optimization-flags=-O2"

I've been using ffmpeg for some Android work too. I do my build a bit different though. I take the lib*.a files and the include dir from the bambuser.com build and just directly include them in my jni directory, my Android.mk looks like this:

LOCAL_PATH := $(call my-dir)

include $(CLEAR_VARS)

LOCAL_MODULE    := ndk1
LOCAL_SRC_FILES := native.c

LOCAL_C_INCLUDES := $(LOCAL_PATH)/include
LOCAL_LDLIBS := -L$(NDK_PLATFORMS_ROOT)/$(TARGET_PLATFORM)/arch-arm/usr/lib -L$(LOCAL_PATH) -lavformat -lavcodec -lavdevice -lavfilter -lavutil -lswscale -llog -ljnigraphics -lz -ldl -lgcc

include $(BUILD_SHARED_LIBRARY)

There might be some cruft in there, but maybe it'll help point you in the right direction. I tried following some of the forms laid out in the NDK example projects like you have. Bundling up the libs into a module and then referencing that. But ended up falling back on the simple direct include just to get things working, and so far haven't had reason to revisit it.